これまでの大学院における研究指導
Past Advisee in Graduate School

• 令和６年度（＠東北大学大学院情報科学研究科博士前期課程　情報基礎科学専攻）
  
  
• Goyal, Akshat　[MEXT Scholar, 2023 Apr.--2025 Mar.]
  Discrete time population dynamics model for exploitative competition between native and alien predators【修士論文】→要旨.pdf
  （固有捕食者と外来捕食者の搾取的競争系についての離散時間個体群動態モデル）
  
  
  Today numerous species are experiencing habitat shifts potentially driven by climate change. Invasion of an alien predator species into a native prey-predator system could lead to substantial ecological consequences. The limiting dynamics of the predator and prey populations are shown to depend substantially on what ages of prey are eaten by predators. Cases havebeen observed where more than one predator species predate on the same prey species but at different life stages. In such cases, new features of biological importance could emerge that are not present in simpler models. They include limits to the length of juvenile periods (both upper and lower) for stability, and the possibility that increases or decreases in any of the modelparameters can be stabilising or destabilising. In large animals only adults participate in direct predation, while sucking feeds on milk from adult predators and juveniles depend on the prey population killed by the adult predators. Conversely, when considered in terms of the prey species, such a stage structure provides more insights in the prey-predator dynamics. In this work we consider a discrete time prey-predator dynamics with an exploitative competition between two predator species sharing the common prey. We examine a scenario where a native prey-predator system is invaded by an alien predator and we will try to discusshow the difference of predation stage could be related to the consequence of the competition for the common prey, especially with respect to the invasion success/failure of the alien predator, while also considering the possibility of coexistence.
  
  
  発表： A population dynamics model of two parasite species competing for the common host with different parasitism stages, A. Goyal, H. Seno, 日本数理生物学会2024年年会（北海道大学 学術交流会館，札幌）, 2024年9月11--13日.   → abstract .pdf
  
  
  
• 服部陽行　Hattori, Haruyuki
  授業中における規範逸脱行動の広がりに関する数理モデルの研究 【修士論文】→要旨.pdf
  （A mathematical model for the spread of rule-breaking behavior in class）
  
  
  授業中に内職を始める生徒がいれば，その行動が教室内で徐々に広がる可能性がある。授業内容とは関係のないそのような行動は規範逸脱行動(rule-breaking behavior)と呼ばれることがあり，教育心理学における研究をはじめとして，多角的な観点からの研究がなされている。本研究では，n×n セルオートマトンによって授業中の教室の空間を数理モデリングし，座席を各セルに対応させる数理モデルを考える。現在の日本の多くの小・中学校，高等学校の各学級の生徒数を勘案すれば6 × 6 セルオートマトンによる数理モデルが現実の教室に対応する大きさをもつ。数理モデリングの仮定として，各生徒が選択する行動は，規範遵守行動(O) もしくは規範逸脱行動(B)のいずれかであり，行動の選択に係る基準(ルール)はどの生徒についても同じであるとする。その基準は，最近接生徒(周りの生徒) のとっている行動の影響を受けて定まる選択行動の価値指数によるものと考える。最小サイズである3 × 3 セルオートマトンモデルについての数学的な解析結果と，6 × 6 セルオートマトンモデルについての数値計算を用いた解析結果により，周りの生徒と同じ行動を選択する傾向が相対的に強い(D < S) 場合，教室内の生徒全員が規範遵守行動をとる状態，あるいは規範逸脱行動をとる状態に至る条件に関する結果を得ることができた。一方，周りの生徒と違う行動を選択する傾向が相対的に強い(D > S) 場合については，授業自体の「雰囲気」に依存して，教室内の生徒全員が規範遵守行動をとる状態に落ち着く場合，教室内の生徒全員が規範逸脱行動をとる状態に陥る場合，教室内で規範遵守行動と規範逸脱行動をとる生徒が併存する状態に至る場合が現れる。本研究では，この数理モデルの解析の数理的な結果に基づいて，教室内における規範逸脱行動の広がりやすさ，広がりにくさの特性についての考察を試みた。
  
  
  発表： 授業中における規範逸脱行動の広がりに関する数理モデルの研究, 服部陽行, 第１０回数理生物学交流発表会 （静岡大学，浜松），2025年3月9--10日.
  
  授業中の規範逸脱行動の広がりに関する数理モデル（A mathematical model for the spread of rule-breaking behavior in class）, 服部陽行, 瀬野裕美, 日本数理生物学会2024年年会（北海道大学 学術交流会館，札幌）, 2024年9月11--13日.   → abstract .pdf
  
  
• 肖陽　Xiao, Yang
  A population dynamics model on the social damage by disinformation spread 【修士論文】→要旨.pdf
  （偽情報の拡散による社会的損害に関する個体群動態モデル）
  
  
  In recent decades, the development of the Internet has made the information exchange much easier and faster than before. Anyone who has a device connected to the Internet can postany piece of information on a platform. Such information can reach another user of the same platform even on the other side of the earth immediately. On the other hand, the spread of a disinformation benefits from the developing Internet facility too. It is not easy for every person to verify the authenticity and accuracy about each piece of information spreading on available platforms. On social occasions like election or in a pandemic situation, people are very easy to encounter various information from unreliable sources. To make matters worse, some people may deliberately spread some disinformation for their own purposes such as attracting public concern or committing fraud. The spread of disinformation has become one of social issues attracting much concern in recent years. Some governments or societies could release some refutation information to suppress the harmful influence of disinformation. In this work, we consider a population dynamics model for the reaction between a piece of disinformation and its counter information in a netizen community. We assume some members of the netizen community who can distinguish disinformation by themselves. When they encounter the disinformation, they can identify its falseness and may communicate others about it. We focus on the population structure in the netizen community, which consists of such “sophisticated” members and the others, and try to discuss how the population structure of a netizen community determines the social damage caused by a disinformation spread in it.
  
  
  発表： A population dynamics model on the social damage by disinformation spread, XIAO Yang, 第１０回数理生物学交流発表会 （静岡大学，浜松），2025年3月9--10日.
  
  A population dynamics model on the social damage by negative information spread, Y. Xiao, H. Seno, 日本数理生物学会2024年年会（北海道大学 学術交流会館，札幌）, 2024年9月11--13日.   → abstract .pdf
  
  

• 令和５年度（＠東北大学大学院情報科学研究科博士後期課程　情報基礎科学専攻）
  
  
• 謝穎　Xie, Ying
  Population dynamics models on the relation of social nature to the epidemics【博士論文】→thesis.pdf
  （感染症伝染ダイナミクスに対する社会特性の関係についての個体群動態モデル）
  
  
  Social nature could have a significant influence on the patterns and trends in the spread of infectious disease. Although it is difficult to quantify the social characteristics, mathematical models have become useful tools forunderstanding the relation of social nature to disease transmission. In this work, we consider three mathematical models incorporating the social naturefrom the aspect of social response, community policy, and the ability to detect the infection of a disease respectively. The analysis of the model with the incorporation of social response, especially assuming that the infection rate is affected by such a response to the disease spread, shows that the social response could become a cause of recurring outbreaks whilst it must suppress the prevalence. From the model for the spread of a reinfectious disease in a community with the acceptance of visitors, particularly under the assumption that a certain proportion of visitors are immune, we findthat the acceptance of visitors could have a significant influence on the disease's endemicity in the community either suppressive or supportive.Furthermore, we consider a mathematical model on the epidemic dynamics of a disease transmission with n strains which follows an order of the competitive dominance according to the infection success in the host. Our model shows that, when no superinfection occurs, the disease becomes eliminated or alternatively the endemic state arises with only the strain which has the largest strain-specific basic reproduction number while all the other strains get eliminated.
  
  
  発表： SIQR model on the disease spread by multiple strains with a competitive dominance, Y. Xie, H. Seno, 日本数理生物学会2024年年会（北海道大学 学術交流会館，札幌），2024年9月11--13日．   → abstract .pdf
  
  SIQR model on the disease spread by multiple strains with a competitive dominance, Y. Xie, H. Seno, Joint annual meeting of the Korean Society for Mathematical Biology and the Society for Mathematical Biology (KonKuk University, Seoul, Republic of Korea), June 30 - July 5, 2024. → abstract.pdf
  
  Xie, Y., Ahmad, I., Ikpe, T.I.S., Sofia, E.F., Seno, H., 2024. What influence could the acceptance of visitors cause on the epidemic dynamics of a reinfectious disease?: A mathematical model, Acta Biotheor., 72(3): 3. https://doi.org/10.1007/s10441-024-09478-w
  
  SIQR model on the disease spread by multiple strains with a competitive dominance, 謝穎, 第９回数理生物学交流発表会 （静岡大学，浜松），2024年3月6--7日.
  
  Relation of the detectability in strains to the endemicity of an infectious disease: A mathematical model, Y. Xie, H. Seno, 日本数理生物学会2023年年会（奈良女子大学，奈良；hybrid開催），2023年9月4--6日．   → abstract .pdf


• Khansai, Nattawut 　[特別訪問研修生 Short-term visiting trainee, 2024 Jan.--2024 Mar.; King Mongkut's University of Technology North Bangkok, Thailand]
  Mathematical models for the analysis and control of the relationship between rice and the brown planthopper by using integrated pest management
  
  
  One rice pest that is considered to be able to cause enormous damage to rice plants is the brown planthopper (BPH). Various strategies have been proposed to control BPH outbreaks, such as cultural control, physical control, chemical control, and biological control. Integrated pest management (IPM) is a method of controlling pests using a variety of strategies to achieve effective and environmentally friendly results. However, the result of using IPM still needs to be studied to determine suitable outcomes for controlling BPH outbreaks. Since laboratory experiments have limitations in many aspects, such as ethics, time, environment, and cost, mathematical modeling is one of options which are used to study the effects of the IPM on BPH infestation. In this article, we present a mathematical model of BPH, with IPM strategies consisting of biological control and chemical control. We used two types of biological control: a natural enemy of BPH and an entomopathogenic fungus. Specifically, Cyrtorhinus lividipennis is considered to be a natural enemy of BPH, and an entomopathogenic fungus is studied as Metarhizium. In addition, we add a chemical control in our model. Next, we prove the existence of positivity and the boundedness of solutions. Equilibrium points and their stabilities are demonstrated as well.
  
  
  発表： Khansai, N., Seno, H., Thamareerat, N., Sirisubtawee, S., Koonprasert, S., Jamboonsri, W., Mathematical modeling for controlling brown planthopper using integrated pest management, WSEAS Transactions on Systems, 23, 2024, 598-618. https://doi.org/10.37394/23202.2024.23.61
  
  A mathematical model for controlling brown planthopper by using integrated pest management: Crytorrhinus lividipennis, Metarhizium, and pesticide, N. Khansai, 第９回数理生物学交流発表会 （静岡大学，浜松），2024年3月6--7日.
  
  


• Schneider, Victor P. 　 [MEXT Scholar in DSPII, 2020 Oct.--2023 Sept.]
  Population dynamics models on the species persistence in the native habitat with the invasion of alien species 【博士論文】（9月修了）→thesis.pdf
  （外来種侵入下の固有生息地における種存続性に関する個体群動態モデル）
  
  
  In the face of ongoing loss of biodiversity and habitat transformations, understanding the complex dynamics governing species survival and competition is critical. This study investigates the interplay of habitat characteristics, such as size and fragmentation, and the invasion of alien species in native habitats. We use mathematical modeling and analysis to tackle the topic, with each chapter addressing a distinct aspect of the issue. We first explore a two patches model of species invasion and competition, highlighting the role of migration rates in determining species survival. We continue onto investigating the impact of habitat size on the success of alien species invasion and survival of native species. Finally, we examine the effect of habitat fragmentation on the persistence of native species. Our results reveal that high immigration rates for the alien species can negatively affect the native species while also increasing the chances of the alien species extinction. Smaller habitats can enhance the prevention of invasion by alien species, particularly when faced with a well-established native species. Additionally, under certain conditions, habitat fragmentation may be beneficial for the survival of native species. These findings challenge traditional models and offer nuanced insights into the complex dynamics of species competition and survival, with implications for both theoretical ecology and practical conservation efforts. This study provides a stepping stone toward a deeper understanding of species interactions and the effects of habitat transformations, advocating for future research that incorporates other environmental factors.
  
  
  発表： Population dynamics model on the persistence of native species in fragmented habitat under an alien species invasion, V. Schneider, H. Seno, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023 TOKYO) (Waseda University, Tokyo), 20 - 25 August, 2023.

  Effect of the Habitat Fragmentation on the Persistence of Native Species against an Alien Invasion, V. Schneider, H. Seno, Tohoku University GP-Chem Chemistry Summer School 2023 in The 9th CWRU x Tohoku Joint Workshop (Tohoku University, Sendai, Japan), 7 - 8 August, 2023.    → abstract.pdf

  Effect of the habitat fragmentation on the persistence of native species against an alien invasion, V. Schneider, H. Seno, The 8th China-India-Japan-Korea International Conference on Mathematical Biology (Sono Belle, Jeju Island, Korea), 27 June - 1 July, 2023.    → abstract.pdf
  
  

• 令和４年度（＠東北大学大学院情報科学研究科博士前期課程　情報基礎科学専攻）
  
  
• 大槻南央　Otsuki, Nao
  他者の利益にただ乗りする者の存在比に関する数理モデル研究【修士論文】→要旨.pdf
  （A mathematical model on the ratio of free-riders for the benefit from the workers' task）
  
  
  社会性昆虫であるアミメアリのコロニーは働きアリの分業で維持されている。若齢の働きアリは繁殖，養育を行い，老齢の働きアリは巣外で獲得した餌を若齢の働きアリに供給する。これらの働きアリは遺伝的に同じ系統であり，進化生物学ではこの場合，老齢の働きアリは若齢の働きアリの繁殖に協力することにより間接的に自身の遺伝子を残すことができていると考える。このような社会構造においては，若齢の働きアリによる繁殖は集団全体の利益（公共利益）を生産する行為であり，老齢の働きアリによる餌の供給は公共利益の生産に協力する行為とみなすことができる。ところが，アミメアリのコロニーには繁殖以外の仕事をほとんどしない異系統が併存する。その異系統の個体は主系統の働きアリが供給する餌を消費し繁殖を行うが，働きアリの系統とは遺伝的に異なるため，進化生物学的にその繁殖は働きアリの利益とならない。さらに，その異系統の子の養育を主系統の働きアリが担っている。つまり，異系統の個体は主系統の個体が協力して餌の供給や子の養育をする社会構造にただ乗りしながら，公共利益の生産には寄与せず自身の利益のみを得ていると考えることができる。Dobata and Tsuji (2013) は，働かないアリ系統の個体の存在が働きアリ系統の個体が形成する集団に与える影響について調べた。彼らは両系統の個体を異なる比率で混合した複数のコロニーを人為的に作製し，均一な条件のもとで64日間飼育した。各コロニー毎に巣内作業と巣外作業の分業個体比率を調べた結果，巣外作業をする働きアリ系統の個体の割合はコロニー中の働かないアリ系統の割合に対して増加した。また，働きアリ系統の個体の生存率や産仔数はコロニー中の働かないアリ系統の割合に対して減少した。これらの結果は，働かないアリ系統の存在が公共利益の生産量を下げ，働きアリ系統はコロニーの状況に応じて分業個体比率を変化させることにより，コロニーを維持していることを示している。アミメアリの社会構造は，公共利益の生産者とその生産に必要な資源を供給する労働者で構成される協力者の集団中に，公共利益を利己的に獲得するただ乗り者が併存する状況として捉えることができる。本研究では，アミメアリの社会構造を事例の一つとして，そのような集団における公共利益生産量がどのようにただ乗り者の影響を受け得るのかを理論的に考察するための数理モデルを構築し，解析結果に基づいた議論を試みた。数理モデルの解析により，協力者中の労働者比率が総公共利益生産量を最大化する値であるとしても，ただ乗り者比率がより大きな集団では，最大総公共利益生産量はより小さくなる結果が得られた。また，巣外作業をする働きアリ系統の割合はコロニー中の働かないアリ系統の割合に対して増加するというDobata and Tsuji (2013) における実験結果に対応するコロニーの条件を導くことにより，彼らの実験におけるアミメアリの集団が働きアリによる産仔効率が高い状況にあったと考え得る理論的示唆が得られた。一方で，餌獲得のし易さや気候による生理的な影響により産仔効率が低い場合には，働きアリの餌供給への分業比率が大きくなり，併存する働かないアリの比率に対して単調減少を示す可能性も示唆された。
  
  
  発表： 協力者の生産する公共利益にただ乗りする者の存在比に関する数理モデル研究：アミメアリの社会構造についての考察，大槻南央， 第８回数理生物学交流発表会（静岡大学；ONLINE開催），2023年3月10--11日.
  
  
  
• 傅 智琼　Fu, Zhiqiong
  A mathematical model on the efficiency of regional lockdown in epidemic dynamics 【修士論文】（9月修了）→要旨.pdf
  （感染症伝染ダイナミクスにおける局所的ロックダウンの効果に関する数理モデル）
  
  
  Lockdown is a strategy to prevent the spread of a trans- missible disease in a community. Especially in countries and regions with poor medical infrastructure and low emergency response capacity, the lockdown will give the government and decision-makers sufficient time to make plans to control the epidemic. Although such a strict restriction has played an important role in suppressing the disease transmission among a community, economic development must tend to face with great challenges, as seen in the COVID-19 pandemic. Furthermore, the prolonged lockdown may cause some problems in the physical and mental health. In this work, we consider a simple mathematical model to theoretically discuss the efficiency of the lockdown, for which we introduce some different types with respect to which social activity is restricted by it. The efficiency is compared according to the endemic size, that is, the number of infective individuals at the endemic equilibrium. Following the results from the analysis on our model, when the isolation period of the regional area is longer than that of the central area, the complete lockdown is the best choice while the weak lockdown is the worst. When the isolation period of the regional area is the same as that of the central area, the weak lockdown is the worst choice. When the isolation period of the regional area is shorter than that of the central area, the strong lockdown is the best choice, while the worst choice depends on the proportion of the infectives of the regional area treated in the central area. When few people takes the medical treatment in the central area, the complete lockdown is better than the weak lockdown.
  
  
  発表： A Mathematical Consideration for the Effect of Regional Lockdown on Endemic Size, Z. Fu, H. Seno, Tohoku University GP-Chem Chemistry Summer School 2023 in The 9th CWRU x Tohoku Joint Workshop (Tohoku University, Sendai, Japan), 7 - 8 August, 2023.    → abstract.pdf
  
  A mathematical consideration for the effect of regional lockdown on endemic size, Z. Fu, H. Seno, The 8th China-India-Japan-Korea International Conference on Mathematical Biology (Sono Belle, Jeju Island, Korea), 27 June - 1 July 1, 2023.    → abstract.pdf
  
  A mathematical consideration on the effect of regional lockdown on the final epidemic size, Z. Fu, H. Seno, 日本数理生物学会第31回大会 (宮崎大学；online開催), 2021年9月13--15日.　　 → abstract.pdf
  
  

• 令和４年度（＠東北大学大学院情報科学研究科博士後期課程　情報基礎科学専攻）
  
  
• Sofia, Elza F. 　
  Mathematical study on the social situation-dependent prevalence in epidemics【博士論文】（9月修了）→thesis.pdf
  （感染症罹患率の社会状況依存に関する数理的研究）
  
  
  Current situation regarding COVID-19 serves as a impetus for a deeper understanding of the community structure and its social characteristics to recognize the risk of infection, which is connected to the epidemic prevalence. Such a huge scale of epidemic is not the first and may not be the last time in history, thus the knowledge of social epidemiology would still be relevant in the distant future. At first, we consider the modeling in which we focused on the local mobility in a regional community and what situations would have the least infection risk. The state of emergency in Japan during April -- May2020 served as an impetus for the consideration of such a modeling. The assumptions were set as such in a state of emergency or semi-lockdown situation where the mobility of people was limited only in a neighbor region that they belong to. According to the report by Parady et al. (2020), shopping is one of the activities with the least reduction in frequency, so setting up the model to consider only the effect of shopping on disease prevalence could be reasonable, as a primitive theoretical consideration on the relation of the infection risk to the social situation. Next, on the modeling for the dependence of the infection risk on community structure, the assumptions were considering the situation, for exampkle, when the lockdown has been relaxed. People are freer to move, however their mobility is dependent on the social structure in the communnity. The community is divided by the activity level and activity phases, and these two factors comprises the social structure in the community. Our analysis of activity level versus the number of new cases served as an initial point to exemplify the tight correlation between these two. Even though these two models are independent, they are complimentary of each other in that they are considering the effect of social situation on the prevalence. What situation would give the larger prevalence? What kind of factors in terms of the community structure would be considered to get the estimation of the social situations according to the severity of an epidemic process? These two questions are commonfor building the assumptions for the models. In Chapter 2, the characteristics of social situation were determined by the preference of shopping. We compared the infection risks in three possible situations: no limitation at all, a certain limitation, and a semi-lockdown with the mobility of limited persons. Semi-lockdown andactivity limitation may not necessarily correlate with a lower infection risk, as is common with the event of superspreader. In Chapter 3, the social characteristics of a community were introducedby the distribution of the community member's activities in terms of the activity level and phase. Communities with young and highly active members will have different challenges from aging communities,although appropriate recognition of the social structure is necessaryfor both cases. Activity center of the community, for example shops,offices, schools, and so on, may benefit from recognizing the activity patterns of its patrons. In such a case, a theoretical game between the activity center and the community members for the least prevalence may be an interesting topic to explore as an extension of this study. As for the modeling in Chapter 2, the theoretical consideration would only work for small communities as large ones would not have only two shops serving the community. The modeling in Chapter 3 may work for big communities, and only activities in the localities were considered. Risks from visitors outside the communities were not taken into account. Only very simple modeling for the infection risk in the private and social phases were used. It was introduced by the simplest functions of the mean density. Disease transmissions do not necessarily require the presence of people, such as the case of droplet transmission.
  
  
  発表： Sofia, E.F., Seno, H., 2023. A mathematical consideration on the relation of the social structure to the infection risk in a community, Interdisciplinary Information Sciences, 29(2): 157-168. https://doi.org/10.4036/iis.2023.R.02
  
  A mathematical consideration on the disease spread in a community with two activity classes, E.F. Sofia, H. Seno, 日本数理生物学会第31回大会 (宮崎大学；online開催), 2021年9月13--15日.　　 → abstract.pdf
  
  A mathematical consideration for disease spread in a community with two activity classes, Elza F. Sofia, 第６回数理生物学交流発表会（静岡大学；ONLINE開催），2021年3月6--7日.
  
  


• Ahmad, Ishfaq 　 [MEXT Scholar in DSPII, 2019 Oct.--2022 Sept.]
  Population dynamics model for the effect of isolation on final epidemic size【博士論文】（9月修了）→thesis.pdf
  （最終感染規模に対する隔離の効果に関する個体群動態モデル）
  
  
  In this thesis, we examine the effect of limited isolation capacity on the final epidemic size, defined as the total number of individuals who had the experienced of the disease. Many countries have faced the difficulty from the shortage of medical resource against the outbreak of SARS-COV-2. When the medical resource is much small, how does the final epidemic size depend on the limited isolation capacity? Our analysis on a mathematical epidemic dynamics model derives a critical value of the isolation capacity below which the isolation reaches the capacity in a finite time in the epidemic season. In such a case, the final epidemic size necessarily becomes larger than that when the isolation capacity is beyond the critical value. Further, we find that the final epidemic size could have a discontinuous jump at the critical of the isolation capacity under a condition about the epidemic dynamics. In such an epidemic dynamics, the isolation capacity below the critical value causes a drastic increase in the final epidemic size,compared to that when the capacity is beyond the critical value. Such a jump in the final epidemic size does not appear under the other condition. Then the isolation capacity below the critical value couldnot result in much increase in the final epidemic size, so that the existence of the critical value of the isolation capacity may be little observable. From the viewpoint of a policy for prevention of a transmissible disease spread, the isolation of detected infectives is one of the possible choices. Our result implies the necessity of a sufficient capacity of the isolation in order that the isolation works effective to suppress the final epidemic size.
  
  
  発表： Ahmad, I., Seno, H., 2023. An epidemic dynamics model with limited isolation capacity, Theory Biosci., 142: 259-273. https://doi.org/10.1007/s12064-023-00399-9
  
  An SIR+Q model with limited capacity of isolation, H. Seno, I. Ahmad, The 8th China-India-Japan-Korea International Conference on Mathematical Biology (Sono Belle, Jeju Island, Korea), 27 June - 1 July 1, 2023.    → abstractpdf.
  
  A model for the effect of limited isolation capacity on the final epidemic size, I. Ahmad, H. Seno, 日本数理生物学会第31回大会 （宮崎大学；online開催），2021年9月13--15日． → abstract.pdf
  
  

• 令和３年度（＠東北大学大学院情報科学研究科博士前期課程　情報基礎科学専攻）
  
  
• Ikpe, ThankGod I.S.
  An epidemic dynamics model in a community with vaccinated visitors during a season 【修士論文】→要旨.pdf
  （ワクチン接種をした訪問滞在者を含む地域における単季節の感染症伝染ダイナミクスモデル）
  
  
  The main purpose of this work is to find out how the acceptance of visitors can affect the dynamics of an infectious disease in a community with an ongoing vaccination program during a season. There are several events and festivities all over the world, that brings visitors from all works of life and various ends of the Earth into one place for a period of time. In the presence of an epidemic outbreak, there is always such skepticism by the host community as to whether to allow visitors or not, the number of visitors to allow, the nature of such allowed visitor. Vaccination or recovery form an infectious disease gives certain level of immunity. This immunity has long been recognized as an important player in breaking the spread of infectious diseases. In this work, we considered the effect of visitors on the spread of an epidemic in a community that has an ongoing vaccination program, with recovered individuals having same immunity level as vaccinated. We especially considered a situation in which a certain proportion of the visitors are vaccinated. Also, we assumed that the immunity gained as a result of either vaccination or recovery is imperfect. Using a modified SIR model, we construct a mathematical model for the dynamics of the resident and visitor population respectively. By analyzing the model, for the case without visitors and also for the case with visitors, we found that the acceptance of visitors could have an effect on the community's tolerance to the infectious disease, depending on the initial tolerance level of the community when there were no visitors. Further, we could show that, for a community that is tolerant to the disease, the acceptance of sufficiently large number of visitors with low proportion of vaccination could cause an outbreak. Also, when the community has outbreak without visitors, under the endemicity, our results implied that a sufficiently large number of visitors may suppress the outbreak.
  
  
  発表： Xie, Y., Ahmad, I., Ikpe, T.I.S., Sofia, E.F., Seno, H., 2024. What influence could the acceptance of visitors cause on the epidemic dynamics of a reinfectious disease?: A mathematical model, Acta Biotheor., 72(3): 3. https://doi.org/10.1007/s10441-024-09478-w
  
  An epidemic dynamics model for reinfectious disease: The influence of visitor acceptance（再感染可能な感染症の伝染ダイナミクスモデル：訪問者受け入れの影響）, Y. Xie, I. Ahmad, T.I.S. Ikpe, E.F. Sofia, and H. Seno, 日本数理生物学会2022年年会（明治大学；ONLINE開催）, 2022年9月5--7日.   → abstract.pdf
  
  

• 令和２年度（＠東北大学大学院情報科学研究科博士後期課程　情報基礎科学専攻）
  
  
• Dansu, Emmanuel J. 　[MEXT Scholar, 2017 Oct.--2020 Sept.; Federal University of Technology, Nigeria]
  Population dynamics modeling for the effect of collective behavior on information spread【博士論文】（9月修了）→thesis.pdf
  （集団挙動が情報拡散に及ぼす影響に関する個体群動態モデリング）
  
  
  Based on the ideas of disease spread dynamics, the thesis examines the diffusion of information subject to certain psychological and sociological situations. We consider two major models, namely a rejoinder model in which there are two interacting pieces of information spreading with a time lag between them and a threshold model in which a person only begins to spread a piece of information after an acceptable number of people have been spreading it. The analysis of the rejoinder model shows that there is a critical time frame within which an individual, organization or government should release information to properly correct misleading information that has been spreading in a population for some time. In addition, the model shows that a critical portion of a population should be targeted with corrective information for it to be effective. From the threshold model, we discovered that the final proportion of knowers of an information is uniquely determined by the initial proportion of knowers in the population. There are also critical proportions and threshold values which determine how well an information spreads within a population. The models provide theoretical frameworks for the promotion of information literacy in order to combat misinformation and disinformation. Information warfare has become intense due to increasing social activities on the internet.
  
  
  発表： Seno, H., Uchioke, R., Dansu, E.J., 2024. A discrete-time population dynamics model for the information spread under the effect of social response, J. Biol. Syst., in press: . https://doi.org/10.1142/S0218339024400072
  
  Dansu, E.J., Seno, H., 2024. A rejoinder model for the population dynamics of the spread of two interacting pieces of information, Afr. Mat., 35: 2. https://doi.org/10.1007/s13370-023-01134-9
  
  Dansu, E.J., Seno, H., 2022. A mathematical model for the dynamics of information spread under the effect of social response, Interdisciplinary Information Sciences, 28(1): 75-93. https://doi.org/10.4036/iis.2022.R.03
  
  A Population Dynamics Model for Information Spread under The Effect of Social Response, E.J. Dansu, H. Seno, The 12th Conference on Dynamical Systems Applied to Biology and Natural Sciences, DSABNS 2021 (online), 2-5 February, 2021.　→ abstract + poster.pdf
  
  A Mathematical Model for The Dynamics of Information Spread under The Effect of Social Response, E.J. Dansu, H. Seno, 日本数理生物学会2020年年会，（名古屋大学；ONLINE開催），2020年9月20--22日.   → abstract.pdf
  
  
  A model for epidemic dynamics in a community with visitor subpopulation
  
  
  With a five dimensional system of ordinary differential equations based on the SIR and SIS models, we consider the dynamics of epidemics in a community which consists of residents and short-stay visitors. Taking different viewpoints to consider public health policies to control the disease, we derive different basic reproduction numbers and clarify their common/different mathematical natures so as to understand their meanings in the dynamics of the epidemic. From our analyses, the short-stay visitor subpopulation could become significant in determining the fate of diseases in the community. Furthermore, our argu- ments demonstrate that it is necessary to choose one variant of basic reproduction number in order to formulate appropriate public health policies.
  

  発表： Dansu, E.J., Seno, H., 2019. A model for epidemic dynamics in a community with visitor subpopulation, J. Theor. Biol., 478: 115-127. https://doi.org/10.1016/j.jtbi.2019.06.020
  
  A Model for Epidemic Dynamics in A Community with Visitor Subpopulation, H. Seno, E. Dansu, 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology (University of Sydney, Sydney, Australia), 8-12 July, 2018.
  
  

• 令和２年度（＠東北大学大学院情報科学研究科博士前期課程　情報基礎科学専攻）
  
  
• 謝穎　Xie, Ying
  A mathematical model for the influence of the social insensitivity on the SIS epidemic dynamics 【修士論文】→要旨.pdf
  （SIS型感染症伝染ダイナミクスにおける社会的鈍感性の影響に関する数理モデル）
  
  
  Individual behavior has long been recognized as playing an important role in an epidemic dynamic. Sometimes such behavior to the disease will not be stimulated unless the epidemic has reached a certain level. The main purpose of this work is to investigate how the social insensitivity affects the epidemic dynamics during the spread of a transmissible disease. From our analysis, we found that the more insensitive to the disease, the larger endemic size is induced. Moreover, the higher sensitivity to the disease may lead to a damped oscillation in the temporal variation of infectives. Our results imply that the social sensitivity and insensitivity would be significantly relevant to the occurrence of such a damped oscillation.
  
  
  発表： Social response could cause recurring epidemic outbreaks: A population dynamics model, Y. Xie, H. Seno, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023 TOKYO) (Waseda University, Tokyo), 20 - 25 August, 2023.
  
  Social Response Could Cause Recurring Epidemic Outbreaks: A Mathematical Model, Y. Xie, H. Seno, Tohoku University GP-Chem Chemistry Summer School 2023 in The 9th CWRU x Tohoku Joint Workshop (Tohoku University, Sendai, Japan), 7 - 8 August, 2023. → abstract.pdf 【Poster Prize受賞】
  
  Social response could cause recurring epidemic outbreaks: A mathematical model, Y. Xie, H. Seno, The 8th China-India-Japan-Korea International Conference on Mathematical Biology (Sono Belle, Jeju Island, Korea), 27 June - 1 July 1, 2023.    → abstract.pdf
  
  A mathematical model for the influence of the social insensitivity on the SIS epidemic dynamics: Occurrence of oscillatory behavior, Y. Xie, H. Seno, 日本数理生物学会2021年年会（宮崎大学；ONLINE開催），2021年9月13--15日.   → abstract.pdf
  
  A mathematical model for the influence of the social insensitivity on the SIS epidemic dynamics，謝穎， 第６回数理生物学交流発表会 （静岡大学；ONLINE開催），2021年3月6--7日.
  
  A Mathematical Model for The Influence of The Social Insensitivity on The Epidemic Dynamics, Y. Xie, H. Seno, 日本数理生物学会2020年年会（名古屋大学；ONLINE開催），2020年9月20--22日.   → abstract.pdf
  
  
  
  
• Schneider, Victor P. 　[COLABS交換留学生, 2019 Oct.--2020 Sept.; Université de Strasbourg, France]
  Mathematical analysis on the effect of temporally changing environment on the structure of an ecosystem【COLABS Report】→manuscript.pdf
  
  
  After a reminder of four very used models in Mathematical ecology, we breach into two different topics. In Chapter 2, we study the phenomenon of apparent competition on a 1 predator species - N prey species system. We prove the conditions for the survival of the prey species or predator species, with the existence of a unique globally asymptotically stable steady state in any case. In Chapter 3, we study the diffusion of a species, first alone, then in a system competing for resources with a motionless species. We use Neumann boundary conditions, but we prove that there is a similarity between this system and a system of one species diffusing with Dirichlet boundary condition. Indeed, here in some cases the motionless species acts as a "death zone" for the diffusing species. Finally by looking at the ratio of the size of the motionless species' habitat and the total size of the patch, we also show the existence of a critical ratio size under which the diffusing species can survive whatever the total size of the patch is.
  
  
  
  
• Högberg, David S. 　[COLABS交換留学生, 2019 Oct.--2020 Sept.; Chalmers University of Technology, Sweden]
  Bipartite lattice model for mycorrhizal networks【COLABS Report】→manuscript.pdf
  
  
  A basic model for mycorrhizal network formation is proposed that specifically examines the effect of spatial heterogeneity and a variable fitness within the population on the resulting degree distribution of the generated network. Trees and fungi are represented as nodes of two different partitions in a bipartite network, where links between each type of node indicate a mutualistic interaction in the form of nutrient exchange. The aim is first and foremost to introduce a basic formalism for studying and reasoning about the structural properties of mycorrhizal networks using network theory.In combination with empirical observations on actual networks, such models may provide valuable insight into why certain patterns are observed under certain environmental conditions.
  
  

• 令和元年度（＠東北大学大学院情報科学研究科博士前期課程　情報基礎科学専攻）
  
  
• 内桶怜奈　Uchioke, Reina
  入学試験倍率の年次変動ダイナミクスに関する数理モデルの研究【修士論文】→要旨.pdf
  （A mathematical model for the annual dynamics of the admission rate）
  
  
  進学における志望校選択は，受験生による意思決定の典型の一つである。今日，日本では受験産業が非常に発達し，受験生は，受験産業から提供される情報を重要な材料として，志望校を決定すると考えられる。本研究では，前年度の受験状況の影響を受けて，受験生が志望校選択の意思決定をする仮定の下で，入学試験倍率の年次変動ダイナミクスに関する基礎的な数理モデルIとIIを構築し，特に，モデルIの解析を行った。 年次変動ダイナミクスモデルIの解析の結果では，受験倍率の隔年変動は現れず，平衡点に漸近していく振る舞いのみが示された。このモデルIの数理モデリングにおける仮定では「受験者の最も多くが集中する学力が前年度の学力平均値で決まる」ことのみが継年の受験状況の間の相関性を与えている。モデルIが表す動態の単純さは，この仮定の数理モデルへの導入の簡潔さが原因であると考えることはできる。モデルIでは導入されなかった因子として，たとえば，受験生の意思決定に関する特性が，学力によって異なっている可能性がある。五十嵐(1999)は，偏差値レベルによって，大学受験への二極分化が起こっており，偏差値が44.9以下の大学では志願者数が減少し，偏差値が55以上の大学では逆に志願者数は増加する傾向にあることについて考察を行っている。また，内田ほか(2018)は，大学入試において，センター試験の自己採点と受験産業が示す大学・学部の難易度データが受験生の志望先の意思決定に強く関わる結果，受験倍率が平準化されることを述べている。たとえば，本論文の数理モデルにおける，定数パラメータが継年的なダイナミクスへの依存性をもつ仮定が導入されるならば，隔年変動の出現の可能性について理論的に考察できる数理モデルが構築できるかもしれない。年次変動ダイナミクスモデルIの解析から，受験者における学力範囲が中庸な場合に，受験者学力平均値の平衡値が最も大きくなる性質が得られた。受験者における学力範囲が広すぎても狭すぎても，受験者学力平均値の平衡値は，その最大値よりは小さい。この結果から，たとえば，受験者の過剰な呼び込みによる受験倍率の上乗せは，受験者学力平均値を下げ，必ずしも，合格者学力平均値を高くしないことが示唆される。また，年次変動ダイナミクスモデルIの解析結果は，受験者学力平均値の平衡値が最大になる状況と合格者学力平均値の平衡値が最大になる条件が一致しないことを示した。学校教育の質を高める上では，合格者学力平均値が高い方が望ましいという見地に立てば，それを実現する上で，受験者学力平均値をより高くすることが，必ずしも適切な選択肢と言えない可能性を示唆している。以上の考察は，年次変動ダイナミクスモデルIの解析結果に基づくものであるが，このモデルIでは受験生の合否が受験時の学力のみで定まっており，入学試験の成績も加味された合否判定とはみなせない。つまり，学力は高いが入学試験で失敗して不合格になる可能性や，学力は高くないが入学試験で努力が実って合格する可能性といった，合否に関する不確定な因子については考慮されていない。本論文では，そのような因子の影響を導入した基礎モデルとして，年次変動ダイナミクスモデルIIを構築した。その解析については今後の課題であり，モデルIとモデルIIの特性の違いを数理的に検討することにより，隔年変動の出現可能性も含めて，受験倍率の年次変動の特性についての考察についてもさらに進めることができると期待できる。
  
  

• 平成２９年度（＠東北大学大学院情報科学研究科博士前期課程　情報基礎科学専攻）
  
  
• 佐藤宏樹　Sato, Hiroki
  昆虫個体群における病原微生物による感染症伝染ダイナミクスの数理モデル研究【修士論文】→要旨.pdf
  （A mathematical model for the epidemic dynamics in the insect population with a pathogenic microbe）
  
  
  昆虫病原微生物であるトノサマバッタ微胞子虫病の病原Antonospora locustaeは，宿主域が広く，90種以上のバッタ類やコオロギ類に感染し，宿主に様々な症状を引き起こす。A. locustaeによる微胞子虫病の感染経路には，垂直感染として，経卵巣伝達と経卵伝達，水平感染として，死骸食を介した感染がある。経卵巣伝達とは，病原微生物が宿主卵巣内で卵母細胞に侵入することにより親から子へ感染する経路，経卵伝達とは，病原微生物が卵表面に付着することにより親から子へ感染する経路のことである。他に，感染個体の糞とともに土中に残存した胞子による経口感染もある。北アメリカでの野外のバッタ個体群におけるA. locustaeによる微胞子虫病の有病率のピーク時期は，バッタ個体群密度のピークから2年遅れて観察されるという（国見・小林, 2014）。本研究では，微胞子虫病の宿主昆虫個体群における感染経路の特性を組み込んだ数理モデリングにより，差分方程式系による数理モデルを構築し，特に，宿主昆虫の個体群サイズの年次変動と微胞子虫病の有病率の年次変動の間の関係に注目しながら，宿主昆虫個体群における微胞子虫病の感染ダイナミクスに関する数理モデル解析を行った。解析の結果，個体群サイズと有病率の年次変動の定常状態は4 つに分類できることがわかった。純増殖率を与えるパラメータR0に着目すると，R0＜1 の場合では，個体群は絶滅に向かう。一方，他のパラメータs（0＜s＜1）に対して，R0 >1/s の場合，個体群サイズは際限なく増大する。1＜R0＜1/s の場合には，個体群サイズの年次変動は正の有限値をとり，ある閾値Rc（＜1/s）より小さい1＜R0＜Rc の場合には定常振動（周期振動もしくはカオス振動）が起こる。Rc＜R0＜1/sの場合には，個体群サイズは正の平衡値へ漸近する。また，文献に報告された実験データに基づいて定めたパラメータ値を用いた数値計算では，個体群サイズの年次変動は定常振動に陥り，その際，個体群サイズがひとたび極大となってから再び極大となるまでの年数である極大年間隔は，6年以上である。より小さなR0 に対して極大年間隔はより長い傾向が得られた。個体群サイズ極大年から直近の有病率最大年までの年数は，ほとんどの場合，2年または3年となった（有病率最大年とは，引き続く2 つの個体群サイズ極大年にはさまれた期間において，有病率が最大となる年である）。この結果は，病原微生物と昆虫個体群の相互作用に関する数理モデルの研究をまとめたAnderson and May (1981) において参照されている実際の昆虫個体群のデータにみられる傾向とも合致している。本研究では，バッタ類の幼虫個体群において見られる共食いによる個体数減少の密度効果は数理モデリングとして組み込んでいないが，死骸食を介した 密度効果を経口感染率の数理モデリングに導入した数理モデルの解析によって，これらの結果を得られたことから，個体群サイズが最大となった2--3 年後に有病率が最大になる現象においては，幼虫期の死骸食を介した経口感染における密度効果がその機序として重要な役割を果たしている可能性が示唆された。
  
  
  発表： 昆虫個体群における病原微生物による感染症伝染ダイナミクスの数理モデル研究，佐藤宏樹， 第４回数理生物学交流発表会，静岡大学浜松キャンパス工学部５号館（浜松），2018年3月2--3日.
  
  バッタ目昆虫の微胞子虫病の感染動態に関する数理モデル研究（A mathematical model for the dynamics of microsporidiosis transmission in Orthoptera），佐藤宏樹・ 瀬野裕美， 日本数理生物学会第27回大会，北海道大学工学部フロンティア応用科学研究棟（札幌），2017年10月6--8日.
  
  


• 平成２２年度（＠広島大学大学院理学研究科博士前期課程　数理分子生命理学専攻）
  
  
• 国貞宗久　Kunisada, Munehisa
  ２株系Kermack-- McKendrick 型SIRモデルにおけるワクチン２種の最適割当問題【修士論文】→要旨.pdf
  （Optimal allocation problem of strain-specific vaccines in Kermack–McKendrick SIR model with two virus strains）
  
  
  新型インフルエンザや季節性インフルエンザに対するワクチンでは，株特異的なワクチンを別々に接種する場合がある。ワクチンの生産や備蓄コストに制限があり，供給総量が限られている場合，病原体２種から成る感染症の流行を最小限に抑えるためには，どのような比率で２株に対するワクチンを備蓄すれば良いだろうか？本研究では，２株系Kermack--McKendrick 型SIRモデルについて，基本再生産数R0を導出し，さらに，２種の株特異的ワクチン接種を導入した場合の拡張モデルについて，数値計算を用いて，ワクチン２種の備蓄割当比率が感染の最終規模（i.e., 被感染者総数）に及ぼす影響について考察した。本研究では，ワクチンの供給総量が（費用や生産性などの制限を受けて）有限な場合の病原体２株による感染症の伝染ダイナミクスに関する数理モデルを考える。ワクチン接種開始後，備蓄されていたワクチンは，ある（有限な）時点において尽きる。ワクチンが尽きるまではワクチン２種の接種を導入した２株系Kermack--Mckendrick型SIRモデル，ワクチンが尽きてからはワクチン接種のない２株系Kermack--Mckendrick型SIRモデルを考える。また，考えている感染症の病原体２株について，株２は株１に対して，相対的に感染性は強いが，感染期間は短い特性をもつものとする。ワクチン投与がない場合の数理モデルについて，株２種から成る感染症の基本再生産数$R_0$の数学的表記を得，感染症が集団に侵入可能となる条件は，それぞれの株毎に定まる，感染力，回復率に依る独立な無次元量によって決まることが明示された。出生・死亡を考えない場合について，数理モデルの数値計算を用いて，感染の最終規模を最小にできるワクチン２種の備蓄割当比率の存在を示すことができた。特に，最適な備蓄割当比率は，一方の株の免疫をもつことによる他方の株感染に対する感受性の変化の程度に強く依存していることが示唆された。また，ワクチン２種の備蓄割合比率に依って，感染規模が相対的に大きくなる場合もあることが示唆された。本研究の結果から，感染規模を抑えるためには，感染症２株における特性の違いに応じたワクチン２種の備蓄割当比率を検討することも予防施策において重要でありうることが示された。不適切な備蓄割当比率の予防施策は予防効果が弱く，感染規模を抑える目 的に対して，不満足な効果しか得られない可能性もあり得ることが示唆される。
  
  In this work, we considered a mathematical model concerning the population dynamics of an infectious disease with two virus strains when the stock of vaccine is limited in the total amount. We derived the basic reproduction number $R_0$ for the Kermack--McKendrick SIR model with two virus strains, and then constructed the below-described SIR model, modifying the Kermack--McKendrick SIR model with introducing the contribution of the vaccination of strain-specific vaccines limited in their total amount. Especially we focused the ratio of those two strain-specific vaccines in the limited stock and considered the optimal ratio to minimize the final size of infected population at the end of epidemic dynamics by the model when the birth and the death processes is negligible so that the total population size is kept constant. After the vaccination starts, the vaccines in the stock become exhausted in a limited time. We obtained the mathematical expression of the basic reproduction number $R_0$ for the model without the vaccination. The $R_0$ is given by two non-dimensional quantities independent from each other, which are respectively determined for each virus strain. Making use of numerical calculations for the model without birth and death terms, we could show the existence of the optimal ratio of strain-specific vaccines in the stock to minimize the final size of infected population at the end of epidemic dynamics. The optimal ratio significantly depends on the degree of the susceptibility to one virus strain when the individual has the immunity for the other strain. Therefore, there could be such a ratio of strain-specific vaccines in the stock as making the final size of infected population larger, too. We conclude that it would be important to consider the ratio of different vaccines in the stock to prevent the outbreak of an infectious disease. The inappropriate ratio of vaccines in the stock may lead unsatisfactory result of the prevention strategy to suppress the outbreak.
  
  
  発表：２株系Kermack--McKendrick型SIRモデルにおけるワクチン２種の最適配分問題 （Optimal Allocation Problem of Strain-Specific Vaccines for a Two Strain Kermack--McKendrick SIR Model），国貞宗久・ 瀬野裕美， 日本数理生物学会第20回大会，北海道大学学術交流会館（札幌），2010年9月13--16日.
  
  


• 平成２１年度（＠広島大学大学院理学研究科博士前期課程　数理分子生命理学専攻）
  
  
• 飛永賢一　Tobinaga, Kenichi
  外来種侵入に対する栄養段階カスケード系の脆弱性に関する数理モデル解析【修士論文】→要旨.pdf
  （A model analysis on the vulnerability of trophic cascade system for alien species invasion）
  
  
  外来種は自然分布域外に意図的あるいは非意図的に導入され，野生化，定着した生物種であり，農業被害，健康・人命被害，生態系への被害をもたらしうる。生産者，消費者，高次消費者の順に相互作用が繋がる系を栄養段階カスケードと呼ぶ。栄養段階上位への外来種の侵入についての報告は少なくないが，対照的に，栄養段階中位への外来種の侵入については報告が少なく，その場合の上位や下位の種に与える影響に関する考察も不十分である。栄養段階中位への外来種の侵入による生態系・生物多様性への影響についてのさらなる研究が必要である。本研究では，「外来生物がどの栄養段階に侵入するか」に焦点を当て，栄養段階中位への外来種の侵入成功性に着目しながら，次に示すLotka--Volterra型相互作用による栄養段階カスケード系モデルを解析し，その結果に基づいて，外来種侵入に対する脆弱性や強堅性に関する栄養段階カスケード系（食物連鎖）の特性についての理論的な考察を行った。数理モデルの解析により，段階$k + 1$への外来種の侵入が成功する条件を導くことができ，外来種の侵入の成功失敗は，外来種侵入以前の平衡状態における，外来 種が利用する栄養段階の平衡生物量によって決まることがわかったので，どの栄養段階への外来種の侵入が相対的に最も難しいかについての平均的な特性を議論するには，外来種侵入以前の系の平衡状態における生物量分布を調べればよい。そこで，本研究では，$n$段階栄養カスケード系の共存平衡点の存在条件を満たすパラメータ領域に着目した。ある2次元パラメータ空間において，$n$段階栄養カスケード系の共存平衡点が存在するパラメータ領域の広さを$S$とする。段階$j$の平衡生物量$N_j^*$が全段階中最大となるパラメータ領域の広さを$S_j^{\textrm{max}}$，$N_j^*$が最小となるパラメータ領域の広さを$S_j^{\textrm{min}}$，$S$に対する$S_j^{\textrm{max}}$, $S_j^{\textrm{min}}$の頻度を，$f_j^{\textrm{max}} = S_j^{\textrm{max}}/S$, $f_j^{\textrm{min}} = S_j^{\textrm{min}}/S$とする$(j=1, 2,?dots, n)$，そして，$f_j^{\textrm{max}}$の大きさを段階$j+1$への外来種の侵入が最も成功しやすい系の存在頻度に，$f_j^{\textrm{min}}$の大きさを段階$j+1$への侵入が最も 成功しにくい系の存在頻度に対応するとみなす。これら$f_j^{\textrm{max}}$, $f_j^{\textrm{min}}$のパラメータ依存性を調べることにより，外来種の侵入に関して，どの栄養段階への侵入が成功し易い，あるいは，成功し難いか，つまり，外来種侵入に対する栄養段階カスケード系の平均的な脆弱性や強堅性について議論することができる。本研究では，特に，$n=3$, $4$, $5$の場合についての詳細な解析を行った。その結果，生産者段階内の密度効果が強い場合に，栄養段階中位への侵入がし難い系の存在頻度が高いことが示唆された．特に，3栄養段階カスケード系では，それが顕著に見られた。結果を総括して検討した結果，より一般的な$n$段階栄養カスケード系においても，この傾向が存在することが示唆された。
  
  We theoretically discuss the vulnerability/tolerance of the trophic cascade system for alien species, analyzing a Lotka--Volterra type of food chain model. As a result of our analysis on the model, the invasion success of alien species is determined by the equilibrium biomass of the trophic level which the alien species consumes. We classify the equilibria with respect to the distribution of equilibrium biomass, in order to determine which trophic level is the most vulnerable/tolerant to the alien invasion. Let $S$ be the area of parameter region for which the coexistent equilibrium exists, according to a two dimensional parameter space. Moreover, let $S_i^{\textrm{max}}$ be the area of parameter region for which the $i$ th trophic level has the largest equilibrium biomass $N_i^*$, and $S_i^{\textrm{min}}$ be that for which it has the smallest equilibrium biomass $N_i^*$. We denote their frequencies by $f_i^{\textrm{max}} = S_i^{\textrm{max}}/S$ and $f_i^{\textrm{min}} = S_i^{\textrm{min}}/S$, and regard them respectively as the frequency of existing trophic cascade systems for which the $j+1$ st trophic level is the most vulnerable to the alien invasion and that for which it is the most tolerant. From their parameter dependence, we find that the system with high tolerance of the intermediate trophic level against the alien invasion could exist with high probability especially when the density effect of producer level is strong.
  
  
  発表：A Model Analysis for The Invasion Success of Alien Species to An Intermediate Trophic Level （外来生物の栄養段階中位への侵入成功性に関する数理モデル解析），飛永賢一・ 瀬野裕美， 日本数理生物学会第19回大会，東京大学数理科学研究科（東京都目黒区），2009年9月9--11日.
  
  


• 平成１９年度（＠広島大学大学院理学研究科博士前期課程　数理分子生命理学専攻）
  
  
• 久保田 聡　Kubota, Satoshi
  自家卵食による最適繁殖戦略に関する数理モデル研究【修士論文】→要旨.pdf
  （Mathematical model consideration for the optimal reproductive strategy with filial cannibalism）
  
  
  親が自分の保護している，あるいは，保護すべき（血縁度1/2の）卵を食べる自家卵食行動（filial cannibalism）は，一般に，オスが卵の世話（保護）をする場合に起こる。卵食された卵から得られる繁殖成功はないが，卵食によって獲得されたエネルギーを成長や生存確率上昇に投資することによって，将来の繁殖成功が有利になる可能性が考えられる。すなわち，卵食に関する現在の繁殖成功と将来の繁殖成功の間にはトレードオフの関係がある。卵食は，生涯繁殖成功度を高めるための適応戦略であると考えられる。テンジクダイ科オオスジイシモチApogon doederleiniの場合は，１繁殖期内に複数回の交尾を行い，メスから受け取った卵塊をオスが口腔内で保育する（口内保育）。Apogon doederleiniの卵食行動として，卵塊全てを食べる全卵食（entire brood cannibalism）と，卵塊の一部を食べる部分卵食（partial brood cannibalism）が観測されており，Takeyama et al. (2002)によって，繁殖期において全卵食の観測される時点の頻度分布が年齢群によって大きく異なる特徴をもつことが報告されている。本研究では，卵食を適応戦略ととらえ，数理モデル解析によって，最適戦略としての卵食の特性を理論的に考察した。特に，卵食をすべきか，せざるべきかだけではなく，卵塊に対する卵食割合を戦略とした数理モデルを構築し，解析した。生涯にわたる期待繁殖成功度の最大化を考えて，各繁殖期における複数回の卵塊保持に対する卵食割合の最適「スケジュール」を考察する数理モデル解析を行うために，将来期待される利得を加味して現在の最適行動を決定するダイナミックプログラミング（動的計画法）の手法を応用した数理モデリングを用いた。数理モデル解析の結果から，卵食割合に関する最適戦略として，部分卵食は起こりにくいことが示唆された。また，本研究では，卵食の発生時期に関して,繁殖期の末期における全卵食は適応的ではないことが示唆されるが，オオスジイシモチApogon dederleiniに関しては，体サイズが大きい，もしくは，年老いた個体が繁殖期の後期に全卵食をする傾向が強いことが観測されており，観測データのすべてを説明できる数理モデルではないことがわかる。本研究の数理モデルでは導入されていなかった，オス個体の生存確率の年齢や体サイズへの依存性や繁殖成功度の実効性比依存性が，実際に観測される戦略の年齢依存性を理解するために重要となる因子かも知れない。
  
  Filial cannibalism is observed in many species of paternal care. It causes the reduction of the current reproductive success, while it increases the advantage in the future reproductive success by investing the obtained/saved energy to the body growth or the survivorship. The cardinal fish Apogon doederleini copulates in several times during each breeding season, and its male cares the brood in its mouth (mouth brooding). Its filial cannibalism is categorized into partial and entire egg cannibalism. It is reported that the distribution of the cannibalism timing during the breeding season is different depending on the male's age class. In this study, we theoretically discuss the optimal strategy of the filial cannibalism, making use of the dynamic programming modelling. Our dynamic programming model is to determine the present optimal behavior taking account of the expected future reproductive success. We mathematically analyze the optimal brood cannibalism schedule of when and how much the male eats the eggs under its care. Our mathematical result implies that the partial egg cannibalism would be hard to be observed, because it is rarely optimal in our mathematical model. Further, by the numerical calculations for our dynamic programming model with the parameter values estimated from the observation data, we examine the optimal strategy of Apogon doederleini. Numerical results indicate that the egg cannibalism is not optimal in the late phase of the breeding season, although the field research observed it especially in the older age class. To understand such brood cannibalism of Apogon doederleini, our model should be extended, for instance, to include the body size dependent or age dependent survival probability, or the sex ratio dependent reproductive success.
  
  
  発表： 自家卵食による最適繁殖戦略に関する数理モデル研究（Mathematical Model Consideration for The Optimal Reproductive Strategy with Filial Cannibalism），久保田聡・ 瀬野裕美，日本数理生物学会第18回大会，同志社大学寒梅館（京都市左京区），2008 年9月16--18日.
  
  
  葉の平行脈の構造に関する数理的研究　
  （Mathematical consideration on the structure of pallarel venation in leaf)
  
  
  単子葉における平行脈の空間パターンの特性について，平行脈の空間分布によって定義される細胞コンパートメントへの物質輸送が空間均一になるという前提により得られる最適空間分布を理論的に検討した。主脈および側脈が輸送する物質総量に対する主脈による輸送物質供給の脈方向での分布に依存して葉全体における側脈の空間分布に違いが出ることが示唆された。側脈の空間分布の違いを用いた葉の形状を適当な仮定を元に作成した結果，ある条件下でのみササの葉の形状に類似のパターンが導出できることが判明した。
  
  Making use of a mathematical model and some observed data, we focus the role of leaf veins to transport the materials for the homeostasis and the photosynthesis in the parallel venation of a bamboo leaf, and consider their optimal spatial distribution in the leaf. In general, the parallel venation is composed with several lateral veins
  and the perpendicular short veins (veinlets) connecting the adjacent lateral ones. Some lateral veins break off or merge into an adjacent one in a middle part of the leaf. We try to understand some features of the spatial vein distribution, and theoretically discuss the optimality. Assuming that the veins are spatially designed to transport the materials equally to every part of the leaf, we find a condition to restrict the number of lateral veins in each part of the leaf for our model.
  

  発表：Spatial Vein Distribution for The Parallel Venation of a Bamboo Leaf: Mathematical Considerations, S. Kubota, H. Seno，SMB/JSMB Joint Meeting (San Jose, CA, USA), July 31 - August 3, 2007.
  
  Spatial Vein Distribution for The Parallel Venation of a Bamboo Leaf: Mathematical Considerations（タケの葉の平行脈の構造に関する数理的研究）, S. Kubota, H. Seno, 理論と実験 研究会（広島大学），2007年10月13 - 14日.
  

  競争系における キーストーン種の存在性に関する数理モデルによる理論研究　
  （Theoretical consideration on the existence of keystone species in a competition system: Analysis for a mathematical model)
  
  
  複数の競争種が共存している系からの1種の削除による系の状態遷移について考える。競争種の削除によって系のバランスが崩れ,派生的な更なる種の絶滅が起こる可能性がある。そのような種の副次絶滅（secondary extinction）が起こるか否かは,削除される種に依存して決まると考えられ,副次絶滅につながる性質をもつ種をキーストーン種と呼ぶ。本研究では,あるLotka-Volterra型N種競争系について,安定共存平衡点にある系から1種を削除した場合に副次絶滅が生起する条件について検討した。全ての種において,同種に及ぼす競争効果が他種に及ぼす競争効果よりも強い場合には,どの種を削除しても副次絶滅は起こらない。副次絶滅が起こりうるのは,ある1種のみについて他種に及ぼす競争効果が同種に及ぼす競争効果よりも強く,他の種については同種に及ぼす競争効果が他種に及ぼす競争効果よりも強い場合に限る。そして,同種に及ぼす競争効果と他種に及ぼす競争効果の強さが同程度である種や競争による影響を受けにくい種が副次絶滅をより生起させ易いことが示された。
  
  In this work, we consider the state transition after deleting a species in the following Lotka-Volterra N species competition system. Shigesada et al.(1984) studied the existence and the stability of its equilibrium states, and found that, after a species deletion in the above system, the secondary extinction of another species could occur due to the collapse of the balance among competing species. The occurrence of such a secondary extinction depends on which species is deleted. We may call the species which deletion causes the secondary extinction the "keystone species". In this work, we focus the condition that the secondary extinction occurs after the deletion of a species in the system at the coexistent equilibrium state. We can find that if the intra-specific competition effect is stronger than the inter-specific one for every competing species, the deletion of any species does not cause the secondary extinction. Only if a certain one species at the equilibrium state has the inter-specific competition effect stronger than the intra-specific one, the secondary extinction could occur. We further find that the secondary extinction is more likely to be caused by the deletion of a species with the intra-specific competition effect compatible to the inter-specific one or by the deletion of a species affected less by the competition effect. This result indicates that there could exist the keystone species in a competition system. In case of the secondary extinction, the number of species which go extinct by a species deletion is uniquely determined. Occurrence of the secondary extinction after the deletion of a species is determined by the composition of competing species, so that its change could affect the possibility of the occurrence of the secondary extinction if a species is deleted or introduced.
  

  発表：Theoretical Consideration on the Existence of Keystone Species in a Competition System: Analysis for a Mathematical Model, S. Kubota, H. Seno，Japanese-Korean Joint Meeting for Mathematical Biology (Fukuoka, Japan), 9月16日−9月18日，2006.
  
  Theoretical Consideration on the Existence of Keystone Species in a Competition System: Analysis for a Mathematical Model, 久保田聡，瀬野裕美，数理分子生命理学専攻　第２回公開シンポジウム　生命科学の新展開　−生命と数理の融合−，広島大学 （東広島），8月， 2006.
  



• 平成１８年度（＠広島大学大学院理学研究科博士前期課程　数理分子生命理学専攻）
  
  
• 松岡 功　Matsuoka, Tsutomu
  格子空間ダイナミクスにおける空間分布の特性を繰り込んだ非標準的平均場近似モデルの考察【修士論文】→要旨.pdf
  （A nonstandard mean-field approximation model involving the characteristics of spatial distribution in the lattice space dynamics）
  
  
  移動スケールに制約のある生物の個体群動態の数理モデリングについては，その空間分布の特性が分布域全体にわたる平均個体群密度の動態に重要な寄与をもつ。そのような個体群動態に対しては格子空間モデルが有効な数理モデルとして用いられてきた。それらは，一般的に確率過程により記述されており，もっぱらコンピュータによる数値計算によって解析されるが，その数値データの理論的な理解の手法として，しばしば，全空間にわたる平均統計量の時間変動のみを差分方程式系もしくは微分方程式系により記述した（標準的）平均場近似モデルを解析した結果との対照が用いられる。しかしながら，空間分布の特性が個体群動態に本質的に重要な寄与を与える場合には，標準的平均場近似モデルは，必ずしも格子空間モデルにおける全空間にわたる平均統計量の時間変動を適切に近似できるとは限らない。本研究では，ある２次元格子空間上の捕食者−被食者系モデルを具体例として，空間分布の特性を繰り込んだ非標準的な平均場近似の開発を試みることにより，格子空間モデルにおける全空間にわたる平均統計量の特性を理論的に理解するための新しい手法の可能性を探ろうとした。提案された新しい非標準的な平均場近似は，理論的な導出によりパラメータ値で一意的に定まる，単純でありながら，格子空間モデルの振る舞いと定性的に近い振る舞いを実現することができるものであり，他の格子空間モデルにも容易に適用できる汎用的な新しいアイデアを提供しているとともに，より一般的な常微分方程式系による個体群動態モデルにおける数理モデリングにも応用できる考え方である。
  
  Interaction such as predation and competition often occurs in a spatial scale much smaller than the scale of spatial population distribution. For some species which mobility is restricted in a specific spatial scale, the characteristics of the spatial population distribution significantly affect the dynamics of the average density over the whole habitat space. The lattice model or the cellular automaton model is useful for modeling such a spatially structured population dynamics. The lattice model is generally analyzed by using the computer simulation. The mean-field approximation model is used in order to analyze the dynamics of the average density over the whole space in the lattice model. However, it does not always give an appropriate approximation. Considering a specific predator-prey system on a two dimensional square lattice space, we develop and propose a non-standard mean-field approximation model involving the characteristics of spatial distribution. Our model gives a more appropriate approximation of the averaged prey density than the standard mean-field approximation model does. In some cases, the proposed non-standard approximation model is more appropriate than the pair approximation model, while our model has a simple structures the mean-field approximation model.
  
  
  個体群削減が離散世代餌−捕食者系の動態特性に及ぼす影響に関する数理モデル解析　
  （Analysis of a mathematical model for the effect of harvesting on the time-discrete prey-predator population dynamics)
  
  
  Beverton-Holt型の密度効果をもつ宿主に対してNicholson-Bailey型の寄生を行う寄生者のなす離散時間host-parasite系に周期的な削減（harvesting）を行った場合の個体群動態の特性について解析した。寄生期間内における削減タイミングも導入した新しい数理モデルの解析の結果，削減がhostのみにかかる場合，parasiteにもかかる場合のいずれの場合も，削減を行った結果，個体群サイズがある平衡値に至る場合には，削減の強さによらず，hostの個体群サイズが増加し，parasiteの個体群サイズが減少することが示された。hostがあるpest speciesである場合を考えると，これは，paradox of pest controlにあたるが，個体群動態における密度効果と削減操作の相互作用によって起こるparadoxであり，削減がhostの天敵であるparasiteに及ばない理想的な場合ですらparadoxが生起することがわかった。このようなparadoxが天敵に対する影響や薬剤耐性の高い個体の増殖といった説明のみならず，個体群相互作用の特性により生起しうることが理論的に示唆された。
  
  We analyze a time-discrete mathematical model of host-parasite population dynamics with harvesting, in which the host can be regarded as a pest. We harvest a portion of the host population at a moment in each parasitism season. The principal target of the harvesting is the host, whereas the parasite population may be also affected and reduced by a portion. Our model involves the Beverton-Holt type density effect in the host dynamics. We investigate the condition in which the harvesting for the host results in an eventual increase of its population, analytically proving that the paradox could occur even when the harvesting does not directly affect the parasite population at all. We show that the paradox of pest control could be caused essentially by the interspecific and the intraspecific density effect.
  

  発表： 人間の介入の効果を含む個体群動態の基礎理論， 瀬野裕美，大談話会（理学研究科数学専攻・情報科学研究科数学教室・WPI-AIMR共催）東北大学WPI 2Fセミナー室（仙台），12月3日，2012.
  
  Matsuoka, T., Seno, H., 2008. Ecological balance in the native population dynamics may cause the paradox of pest control with harvesting, J. Theor. Biol., 252: 87-97.
  
  Indirect Effect May Cause The Paradox of Pest Control, H. Seno, T. Matsuoka, BIOCOMP2007 — Collective Dynamics: Topics on Competition and Cooperation in the Biosciences（Lloyd's Baia Hotel, Vietri sul Mare, Salerno,Italy）, September 24 - September 28, 2007.
  
  Interspecific Reaction May Cause The Paradox of Pest Control, H. Seno, T. Matsuoka, ReaDiLab Conference "Mathematical modeling and analysis in biological and chemical systems" (University of Paris-Sud XI, Orsay, and IHES, Bures-sur-Yvette, France), September 3 - September 5, 2007.
  
  Density Effect May Cause The Paradox of Pest Control, T. Matsuoka, H. Seno, The 2nd Dynamical Systems Theory and Its Applications to Biology and Environmental Sciences（第２回「力学系理論と生物学・環境科学への応用」国際シンポジューム） (静岡大学システム工学科・佐鳴会館，Hamamatsu, Japan), 14-17 March, 2007.
  
  Interspecific Reaction May Cause The Paradox of Pest Control, H. Seno, T. Matsuoka, SMB/JSMB Joint Meeting (San Jose, CA, USA), July 31-August 3, 2007.
  
  Analysis of a Mathematical Model for the Effect of Harvesting on the Time-Discrete Prey-Predator Population Dynamics, T. Matsuoka, H. Seno, Japanese-Korean Joint Meeting for Mathematical Biology (Fukuoka, Japan), 16-18 September, 2006. 【Poster Prize受賞】
  

  食物連鎖におけ るエネルギー栄養段階の数に関する数理モデル解析
  （A mathematical model for the number of energy trophic levels in food chain)
  
  
  生態系では，緑色植物などが光合成によって生成したエネルギーは，栄養段階と呼ばれる段階を移動する。第1栄養段階は光合成によりエネルギーを生成する生物，第2段階は植食動物，第3段階以上は肉食動物から成る。本研究では，数理モデルの解析によって，安定に存在できる食物連鎖を成す栄養段階の数に関しての理論的考察を行った。エネルギー生産量が植物及び植食動物の増減に依存しない，定常な環境を仮定し，第1段階におけるエネルギー生産率を一定値とする。確立する段階数は，エネルギー生産率に依存して決まり，無限の段階数も確立され得ることが，数学的に証明できる。また，存在し得る食物連鎖の長さが有限な上限をもつ条件も導くことができる。特に，各パラメータが栄養段階に依らず全て等しい場合には，無限段階数の食物連鎖は確立され得ない。この場合，可能な最長の食物連鎖において，各段階に存在するエネルギー量の分布は，必ず，下位ほど大きいピラミッド構造を示す。しかし，最上位の段階を取り除くと，ピラミッド構造は崩れる。それでも，偶奇段階のそれぞれについては，その単調性は維持されている。本研究では，栄養段階数及びエネルギー量の分布について，さらに詳細な解析結果を体系的にとりまとめた。その結果，エネルギー栄養段階については，ピラミッド構造は，必ずしも一般的とは言えないことがわかった。
  
  We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases, we find that the possibly longest chain is such that the lower trophic level has a greater energy reserve than the higher has, so that the distribution of energy reserves can be regarded to have a pyramid shape, whereas, if any of its trophic levels is removed, the pyramid shape cannot be maintained. Further, we find the condition that arbitrary long chain can be established. In such unbounded case, we prove that any chain could not have the pyramid shape of energy reserve distribution.
  

  発表：Matsuoka, T., Seno, H., 2008. Possibly longest food chain: analysis of a mathematical model, Math. Model. Nat. Phenom., 3(4): 131-160.
  
  Length of Food Chain: Analysis of a Mathematical Model, T. Matsuoka, H. Seno, International Conference on Ecological Modelling 2006 in Yamaguchi, Yamaguchi University, Ube, Yamaguchi, Japan, 2006年8月28日-9月1日.
  
  Length of Food Chain: Analysis of a Mathematical Model，松岡功，瀬野裕美，数理分子生命理学専攻　第２回公開シンポジウム　生命科学の新展開　−生命と数理の融合 −，広島大学（東広島），8月， 2006．
  
  食物連鎖におけるエネルギー栄養段階の数に関する数理モデル解析（A Mathematical Model for The Number of Energy Trophic Levels in Food Chain），松岡功・瀬野裕美，日本数理生物学会第15回大会（2005年数理生物学シンポジウム），横浜国立大学 （横浜），9月15日 −9月17日，2005.
  



• 平成１５年度（＠広島大学大学院理学研究科博士前期課程　数理分子生命理学専攻）
  
  
• 緒方直美　Ogata, Naomi
  タンパク質相互関係ネットワークグラフの幾何的構造における次数分布に関する数理モデルの構築と解析【修士論文】→要旨.pdf
  （Construction and analysis of mathematical model for the degree distribution in geometric structure of protein interaction network graph）
  
  
  Since the discovery of the structure of protein molecule, a dominant view of molecular biology has been the understanding of microscopic mechanisms operating at the gene level. But, in our work, we focus not any individual protein but the network of protein interactions. Especially we consider its geometric structure. Protein interaction network consists of {\bf nodes} (proteins) and {\bf links} (interactions between proteins). {\bf Distance} of two nodes in it is defined by the smallest number of links tracing from one to another. {\bf Degree} of each node is defined by the number of its links. In this work, we considered the mathematical model, a sort of what called the network growth model. Network grows by itself in discrete time step with the following process: (1) Node duplication]Randomly selected node in the network is duplicated and creates a new node. The new node has the same links as its original node; (2) "Link deletion" Some links in the network are deleted with probability $\delta$; (3) "Link creation" Some links are created with probability $\alpha$. In our work, we constructed and considered a new model called {\bf Duplication+$q$-Diversification (D$q$D) model}: Link deletion occurs alternatively for the link of new or its original node, so that one of their corresponding links is delated with probability $?delta$ and another remains to a common node remains with probability 1. Link creation occurs with probability $\alpha$ between the new node and those nodes of distance 2 to $q$. In the D$q$D model, with an appropriate mean-field type of approximation, we consider the expected value of degree in network of $N$ nodes and the degree distribution $\{P_N(k)|k=0,1,2,\cdots,N-1\}$, and derived the approximated equations that determine them according to the network size $N$. Analyzing these approximate equations, we tried to examine the geometric features of growing network in the D$q$D model. With the hypothesis that the mean degree would asymptotically converge a finite positive value as the network size gets larger, we carried out our analysis, and found that those models studied in previous works and ours are classified into two categories in terms of the mean degree in a sufficiently large network: One is such that the change of geometric features of network gradually becomes restricted local as the network gets larger, while another is such that the local change could cause a global transition of whole network, even in the large network. We consequently arrived at the conjecture that such classification of growing networks could be applied for the evolutionary process of real protein interaction network.
  
  
  発表：緒方直美，瀬野裕美，タンパク質相互関係ネットワークグラフの幾何的構造における次数分布に関する数理モデルの構築と解析 （Construction and Analysis of Mathematical Model for the Degree Distribution in Geometric Structure of Protein Interaction Network Graph），日本数理生物学会 第14回大会（2004年数理生物学シンポジウム），広島大学学士会館（広島県東広島市）2004年9月. → abstract.pdf
  
  
  パッチ状環境内での移住における好みの効果を導入した個体群動態モデル　→草稿.pdf
  （Population dynamics introduced the effect of biased migration in patchy environment)
  
  
  We consider the dynamics of single-species population migrating within a fragmented habitat, focusing the effect of characteristics of dispersing tendency on the total population size. We analyze a simple mathematical model in which the population within each patch grows following the logistic equation with parameters depending on the environment within the patch, and the emigration rate depends on which patch the disperser emigrates from. As for the immigration rate, it depends on the population density of destination patch and the density-independent patch-preference. Especially we examine the effect of disperser's patch-preference on the total population size in the whole habitat, and discuss the feature of specific patch-preference to maximize (or minimize) the total population size, analyzing the model with numerical calculations and some mathematical analysis. We consider the biological meanings of such specific patch-preference, and conclude that the patch-preference could significantly affect the total population size.
  

  発表：緒方直美，瀬野裕美，パッチ状環境内での移住における好みの効果を導入した個体群動態モデル（Population Dynamics Introduced the Effect of Biased Migration in Patchy Environment），第13回数理生物学シンポジウム，奈良女子大学（奈良），2003年9月． → abstract.pdf
  
  緒方直美，瀬野裕美，パッチ状環境内での移住における好みの効果を導入した個体群動態モデル （Population Dynamics Introduced the Effect of Biased Migration in Patchy Environment），数理分子生命理学専攻　第１回公開シンポジウム　生命科学の新展開　−生命と数理の融合−， 広島大学学士会館（広島県東広島市）2003年8月.
  



• 平成１０年度（＠奈良女子大学大学院理学研究科修士課程　情報科学専攻）
  
  
• 中山木綿　Nakayama, Yu
  植物個体群における２倍体と３倍体の共存に関する数理モデル解析【修士論文】
  （Mathematical considerations for coexistence of diploid and triploid in a single plant population）
  
  
  Plants that can reproduce both sexually and agamically are called facultative apomicts. Some species, such as {?it Taraxacum}, contain both sexual diploids and triploid facultative apomicts. Triploids produce seeds without gamete fusion and recombination, and can also produce pollen and fertilize diploids. We present a population dynamic model that deals with gene flow and competition between diploids and triploids, with differing allocation towards reproductive investment in seeds and pollen. This paper examines whether diploids and triploids of plants with facultative agamospermy can coexist within a single population. We analyse the global behavior of such a dynamic system. Features of the system are significantly affected by the germination rates of diploids and triploids. Either diploids or triploids persist alone when the germination rate of diploids is sufficiently larger or smaller than that of triploids, respectively. Competitive exclusion occurs when both germination rates are sufficiently large. Coexistence is possible under certain specific conditions when: (I) the germination rates of both diploid sexuals and triploids are not sufficiently large, and (II) triploids produce sufficient pollen. When diploid sexuals and triploids coexist, triploids cannot exist alone, implying that the pollen of triploids is necessary to exploit diploid ovules.

  発表： Nakayama, Y., Seno, H., Matsuda, H., 2002. A population dynamic model for facultative agamosperms, J. Theor. Biol., 215: 253-262．
  
  中山木綿，瀬野裕美，松田裕之，2倍体とアポミクト3倍体の共存可能性に関する数理的研究，日本進化学会第2回大会，東京大学教養学部（駒場キャンパス）（東京 都目黒区）2000年10月.
  
  中山木綿，瀬野裕美，松田裕之， 植物個体群における２倍体とアポミクト３倍体の共存可能性， 第９回数理生物学シンポジウム，東京大学大学院数理科学研究科（東京都目黒区）1999年10月. → abstract.pdf
  

  娘の停留性が繁殖に有利なのはどのような環境か？
  （What environment makes the daughter stay in her mother's home range?）
  

  Dominant-subordinant relationships in Formosan squirrel are different between the native habitat and the other (Tamura {?it et al.}, 1989). In the natal habita located a Ken-ting National Park in Formosa, the subordinate, that is the daughter, could reproduce offsprings in her mother's home range. At Kamakura city in Japan, the daughter could not reproduce offsprings in her mother's home range, instead could help mother's breeding offsprings. In this paper, we theoretically discuss why such difference could occur, making use of a mathematical model. At Kamakura ( an immigrated area), daughters settle adjacent to the mother's home range or inherit it, and never share it with each other. In sontrast, at Ken-ting, daughters share a common home range with their mother. These two habitats are suggested to have some differences about food availability and predation risk. Habitat at Kamakura has relatively less food and fewer potential predators. At Ken-ting, it provides sufficient food throughout year. In the present study, we theoretically show that the tolerance between mother and daughters in the native habitat would be probably resulted in because of the richness of available food.
  

  発表：中山木綿，瀬野裕美，停留性の娘が繁殖に有利なのはどのような環境か？，第８回数理生物学シンポジウム　研究集会 Mathematical Topics in Biology，京都大学数理解析研究所，1998年10月． → abstract.pdf



• 平成９年度（＠奈良女子大学大学院理学研究科修士課程　情報科学専攻）
  
  
  • 佐藤葉子　Sato, Yoko
    姓の存続と絶滅についての数理的考察【修士論文】→summary.pdf
    （Mathematical considerations for persistence and extinction of family names）
    
    
    We consider in this paper how the number of people in a family line with the same family name increases or decreases by chance from a probabilistic viewpoint: The number of children born from a couple could be regarded as stochastic event. Theoretical arguments about this problem were first given by H.W. Watson and followed by F. Galton in the end of the last century (Watson and Lotka, 1874; Galton, 1891). Their mathematical modelling assumed that all men had the same length of life and that their family lines were succeeded by their sons. Exchange of members of any generation to the next was occurred at the same moment. How many of sons a man has in his life was stochastically determined with a probability distribution. The process is called the Galton-Watson branching process. Another possible modelling way is the age-dependent branching process. In the process, the life length of each member in a family line is independent of that of any other, and the life length of each member follows a probability distribution. Replacement between the subsequent generations does not occur simultaneously in general, differently from the Galton-Watson process. As in the Galton-Watson process, the number of sons follows a probability distribution, and the family lines are succeeded from fathers to their sons. In this thesis, for the mathematical modelings with the Galton-Watson branching process and the age-dependent branching process, we assume that the successor, regardless of sex, inherits the considered family name, and we mathematically discuss some problems about the persistence and the extinction of family names. We further consider the probability distribution of the number of successors, taking account of the birth rate, the sex ratio and the succession rate of family name succession. With our mathematical models, we discuss the effect of the rate of family name on the persistence. Moreover, we consider the case when the successor rate of family name depends on the sex of successor, if both sexes of child could become the successor of family name. To try to give some perspectives with respect to the persistence of the present Japanese family names, we estimate the probability of extinction of family name, making use of some statistical data and the theoretical results by mathematical modelling with branching process. As a result, the probability of extinction of family name in Japan is smaller than 1 and the probability with which family name persists is not zero at present. With some mathematical results by the modelling analyses, we consider the effect of sex ratio and unmarried ratio of the present successors on the probability for the ultimate extinction of family name. When a family name is succeeded from a father to his sons, if the male ratio in the children is higher, the probability of extinction of the family name is smaller. As the unmarried ratio gets higher, the probability is higher. In the present Japan, we can find so many family names. We analyze the characteristic natures of the frequency distribution of Japanese family names, using the data of family names by Meiji Life Insurance Company. We find a rank-size relation called Zipf's law for the frequency distribution of family names. Furthermore, using the Simpson's index of diversity and the Shannon-Weaver function, we try to discuss the diversity of family names in Japan.
    

    発表： 佐藤葉子・瀬野裕美著「姓の継承と絶滅の数理生態学 --- Galton-Watson分枝過程によるモデル解析」， 京都大学学術出版会, 2003，pp. 234．
    
    瀬野裕美，佐藤葉子， Galton-Watson分枝過程による姓の存続性に関する数理モデル解析：日本の姓の存続性， 日本応用数理学会199９年度年会，愛媛大学工学部（愛媛県松山市）1999年10月．

    瀬野裕美，佐藤葉子， Galton-Watson分枝過程による姓の存続性に関する数理モデル解析， 第９回数理生物学シンポジウム，東京大学大学院数理科学研究科（東京都目黒区）1999年10月． → abstract.pdf

    Seno, H., Sato,Y., Mathematical Considerations on Persistence of Japanese Family Names: Effect of Sex-Biased Inheritance, The International Conference on Theory and Mathematics in Biology and Medicine 1999, Vrije Universiteit Amsterdam, The Netherlands, 29 June-3 July, 1999.
    
    Seno, H., Sato, Y., Mathematical Modelling Analysis on Persistence and Extinction of Family Names, International Symposium on Power-Law Modelling of Biological Systems, Oeiras, Portugal, 4-7 October, 1998. → abstract.pdf
    

    Mathematical modelling considerations for the optimal shell change of hermit crabs
    （ヤドカリの殻交換の最適タイミングに関する数理モデル解析）
    
    
    Shell kept by the adult hermit crab has some important roles for its life. The shell is a shelter for the individual and its eggs against predation. The kept shell size often limits the body size of the owner. To grow up to the larger body size, the individual should change the shell to another larger one. If the individual cannot get another larger one, the individual has to suppress the body size growth as the owned shell size allows. The individual with the larger body size has an advantage over the smaller individual. Suppression of the size growth can be regarded as to result in the less reproductive success. To consider the maximization fo the reproductive success, we define the energy reserve of individual, which could change due to the energy input and output by feeding, homeostasis, and the shell change behaviour. With some mathematical modelling, we consider the criterion about whether the individual should try to change the shell or not. We discuss what and how factors influence the shell change optimality and timing for the behaviour, when the individual should change the shell. We show that the optimality of shell change behaviour has relation with the length of shell change-allowed season and the body size. They also affect the optimal timing of shell change. It is implied that the probability of successful shell change and the cost for the shell change behaviour do not affect the optimal timing of shell change at all but significantly do the optimality of behaviour.

    発表： Sato, Y., Seno, H., 2006. A mathematical consideration for the optimal shell change of hermit crab, J. Theor. Biol., 240: 14-23.
    
    佐藤葉子， 瀬野裕美，ヤドカリの殻交換の最適タイミングに関する数理モデル解析， 第７回数理生物学シンポジウム，大阪大学，1997年10月12-14日． → abstract.pdf

  
  
• 平成７年度（＠広島大学大学院理学研究科博士前期課程　数学専攻）
  
  
  • 河内健治　Kouchi, Kenji
    Dynamical considerations on optimal diet selection theory.【修士論文】
    （最適餌選択理論に関する動的考察）
    
    
    Foraging predators always face important alternative judgements to determine whether or not to catch the prey when they encounter it. If the predator catches every pary without such judgement, it might gain little income and waste energy and time since some preys might contain little energy or require relatively long time for predator to catch, eat and digest them. In contrast, with another excessive judgement, if the predator forages only high-quality preys which have relatively low density, the predation could not satisfy its metabolic needs. So predator needs some criteria for the foraging strategy depending on both quality and density of prey. The optimal diet selection theory argues how and which prey a predator should catch and eat in order to maximize the expected energy intake rate. The optimal diet selection theory stands on the stationary invariant environment and circumstance so as to consider the ideal behaviour of predator: dynamical factors, for example, densities of predator and prey, are set constant. In reality, those densities are always changing dynamically because of predation, growth, environmental fluctuation and so on. Under such circumstances, the optimal diet menu determined by the classical theory is not always optimal for predator. Then, the aim of this paper is to study the theory from the dynamical viewpoints. We review the classic theory and try to argue some dynamical aspects extended from it. Then we construct and analyze the dynamical model, making use of population dynamics model.
    
  
  
  • 平田久也　Hirata, Hisaya
    How related is the size distribution of mating groups to the existence and the frequency of sneakers?: Some mathematical modeling analyses.【修士論文】→thesis.pdf
    （繁殖集団のサイズ分布形とスニーカーの存在・頻度との間にどのような関係があるか？：数理モデルからの考察）
    
    
    In this paper, at first, we considered how the size distribution of mating groups is related to the existence of sneakers. We constructed and analyzed a mathematical model for the invasion of sneaking strategy against the mating group strategy, and discuss how the invasion success depends on the size distribution of mating groups. We obtained the result that as the variance of the distribution gets smaller, the existence of sneaker becomes difficult. When the population of the sneaker is established, how related is the size distribution of mating groups to the frequency of sneakers in the population? In Chapter 3, we constructed and analyzed a mathematical model for the coexistence of the mating group strategy and the sneaking one, and discuss the dependence of the frequency of sneakers on the size distribution of mating groups. Even if it is disadvantage for the sneaker, the ratio of sneakers can get large. For example, we analyzed how the variance of the distribution depends on the ratio of sneakers and the sex ratio. In the range of large variance of the distribution, sneakers decrease the competition for a mating in them by decreasing the population of themselves, and increase their fitness. While, in the range of small variance, sneakers intercept the matings of territorial male by increasing their population and decrease the fitness of territorial males, and increase their fitness relatively. That is, the sneaker make the advantage for theirselves by interfering the territorial male. Thus we analyzed the ratio of sneakers and the sex ratio derived from our model and showed that it would be also significantly affected by the size distribution of mating groups.
    
    発表：平田久也，瀬野裕美， How related is the size distribution of mating groups to the existence and the frequency of sneakers，研究集会Mathematical Topics in Biology，京都大学数理解析研究所，1996年6月13-15日．
    
    平田久也，繁殖集団のサイズ分布形とスニーカーの存在・頻度との間にどのような関係があるか？：数理モデルからの考察，大域情報セミナー（奈良女子大学理学部情報科学科），奈良女子大学，1996年3月16日.

    How does the size distribution of male territories depend on the spatial distribution of females? →manuscript.pdf
    （雄の成す縄張りのサイズ分布は，メスの空間分布にどのように依存するか？）
    

    We consider the relation between the spatial distribution of resource related to the mating activity, for instance, the spatially distributed females themselves and the size distribution of territories established by males for purpose of mating. Assuming the ranking related to the position of territory, we construct and analyze a mathematical model to consider how the spatial size distributions of the territories and the mating groups are affected by the spatial distribution of mating resource. Our modelling analyses clearly demonstrate that the size distribution of territories is significantly affected by the spatial distribution of mating resource. The tendency of the spatial size distribution of territories is monotonically increasing for some types of spatial distribution of mating resource as the territorial site gets located far from the most favorable place, while a specific spatial distribution of mating resource can realize a monotonically decreasing size distribution of territories.
    

    発表： Hirata, H., Seno, H., 1997. How does the size distribution of male territories depend on the spatial distribution of females?, Ecol. Modelling, 103: 193-207.

    Dynamics of population scrambling for limited number of available territory sites. →draft.pdf
    （有限個の縄張りを奪い合う個体群のダイナミクス）
    

    In this paper, we consider a mathematical model for the territorial population scrambling for the territory. In our modelling, we classify the considered population into two subpopulations: territorial and non-territorial, and further, do each of these subpopulations into non-fighting territorial population and fighting. The considered region is assumed to involve the suitable habitats and unsuitable ones for the successful reproductive activity. We consider the effect of change of the availability of suitable habitat, that is, the proportion of suitable habitats in the considered region, on the persistence and the structure of population scrambling for the territory. Especially, we discuss the threshold for the availability of suitable habitats according to the persistence of population, and the dependence of the structure of population and the occupancy ratios of the suitable habitats at the equilibrium state on the availability of suitable habitats.
    

    発表：平田久也，Dynamics of Population Scrambling for Limited Number of Available Territory Sites（有限個の縄張りを奪い合う個体群のダイナミクス），第18回数理生物談話会，同志社大学今出川校舎ハリス理化学会館，1995年12月16 日.

  
  
  • 丸山淳司　Maruyama, Junji
    Mathematical modelling for the intra-specific brood-parasitism: The optimal strategy for the parasitism and the coexistence between host and parasite.【修士論文】→要旨.pdf
    （種内托卵に関する数理モデル解析：托卵者の最適戦略と托卵者と仮親の共存様式）
    
    
    For a number of species of birds, brood-parasitism by laying eggs in the nest of the other individuals has been reported. There are two categories of such nest parasitism: One is inter-specific brood-parasitism in which eggs are laid in the nest of different species, and another is intra-specific brood-parasitism in which eggs are laid in the nest of the other individual of the same species. Moorhen is one species to show the intra-specific blood-parasitism. It inhabits all over the world except for Australia. In this work, we at first consider the optimal strategy for the intra-specific brood-parasitism, especially according to the number of eggs laid by the parasite in the nest of host that does not reject the parasite's eggs. With a mathematical model, assuming that the survival probability of parasite's offsprings in the nest of host is significantly smaller than in the nest of parasite own, we argue the optimal number of eggs laid in the nest of host to maximize the expected fitness for the parasite. Next we consider a mathematical modelling for the intra-specific brood-parasitism for the coexistence between parasite and non-parasite individuals within a population. We can consider that such behavioral consequence is to gain the possibly highest fitness. With a mathematical modelling analysis, we try to argue on why and how parasite and non-parasite individuals could coexist in the population of moorhen. We show that the invasion success of brood-parasitism could significantly depend on the total number of eggs laid by the parasite in a breeding season, and that the successfully invading brood-parasitism could realize maximum fitness with a specific number of parasite's eggs laid in the nest of the host. As for the condition in order that parasite individuals coexist with non-parasite ones within a population, it is shown that the stable equilibrium frequency of parasite individuals within a population, if exists, depends on the difference among individuals in terms of the individual quality reflected to the survival probability of bred offsprings.
    

    発表： Maruyama, J., Seno, H., 1999. The optimal strategy for brood-parasitism: How many eggs should be laid in the host's nest?, Math. Biosci., 161: 43-63.

    Maruyama, J., Seno, H., 1999. Mathematical modelling for intra-specific brood-parasitism: Optimal parasitism strategy and host-parasite coexistence, Math. Biosci., 156: 315-338.

    瀬野裕美，抱卵と托卵を共に行う個体の最適托卵戦略からみた托卵行動の進化，京都大学生態学研究センター公募研究会「ホスト−パラサイト系の動態と進化に関する数理的研究」（代表者：梯正之，広島大学医学部），京都大学，1998年11月.
    
    Seno, H., Maruyama, J., The Optimal Strategy for Brood-parasitism: How Many Eggs Should be Parasitized?, "FROM INDIVIDUALS TO POPULATIONS", International Workshop and Young Scientists School, Ceske Budejovice, Czech Republic, 10-14 August, 1998.

    Seno, H., Maruyama, J., Mathematical Modelling for Intra-specific Brood-parasitism: Coexistence between Parasite and Non-parasite, International Conference on Deterministic and Stochastic Modelling of Biointeraction, Sofia, Bulgaria, 28-31 August, 1997.
    
    丸山淳司，種内托卵に関する数理モデル解析：托卵者の最適戦略と托卵者と仮親の共存様式，大域情報セミナー（奈良女子大学理学部情報科学科），奈良女子大学，1996年3月16日.
    

    Some aspects of Hawk-Dove game with relatedness. →draft.pdf
    （近縁度を導入したタカハトゲームに関する考察）
    

    In this paper, with the notion of inclusive fitness, we reconsider the Hawk-Dove game which Maynard Smith and Price considered. In the traditional Hawk–Dove game, two types of individual are assumed in the considered population: one takes Hawk strategy and another takes Dove strategy. Hawk strategy is such that the individual fights until it wins or is beaten. Dove strategy is the strategy that the individual does not want to fight and runs away if the rival challenges him to fight. Now, we assume that two individuals fight over the food with its value $V$, which means that the fitness of the individual who gets the food increases by $V$. There are three cases of fight, (1) Hawk vs Hawk; (2) Hawk vs Dove; (3) Dove vs Dove: In the case that Hawk vs Hawk, the fight goes on until one of them is beaten and runs away. Individual alternatively wins or is beaten with the probability 1/2. The fitness of the winner increases by $V$ and that of the loser decreases by $C$ due to the cost for the fight. Hence, the expected gain for the Hawk individual in this case is $(V −C)/2$. In the case that Hawk vs Dove, Hawk always defeats Dove. Therefore, the expected gain of Hawk is $V$, while that for Dove is 0 because he runs away before wounded. In the case that Dove vs Dove, they always share the food. Therefore, the expected gain for each of them is $V/2$. Maynard Smith and Price considered two types of strategy (Maynard Smith and Price 1973): One is the pure strategy, and another is the mixed one. Pure strategy is such that every individual can take only one specific strategy, Hawk or Dove strategy. Mixed one is such that every individual takes Hawk strategy with probability $P$ and Dove one with probability $1 − P$. They also defined the evolutionary stable strategy (ESS) as follows: If almost all members take the strategy, no mutants who take the strategy different from it can have the higher fitness and increase within the population. In our work, we found that whether the stationary frequencies of the Hawk and Dove groups depend on not only the benefit of foods and the cost of fight but also the relatedness. In the case that an individual takes only one of Hawk and Dove strategies, it is possible only when the individuals in the same group have the common gene that Hawk group occupy the population. In the case that an individual takes mixed strategy, it is hardly possible that the frequency of the mutants which are a little more aggressive than others increase. However, when $C > V$, it is possible that the mutants occupy the population.
    


• 平成６年度（＠広島大学大学院理学研究科博士前期課程　数学専攻）
  
  
  • 小出千絵　 Koide, Chie
    SIR modelling analysis on asymmetric transmission of heterosexual disease.【修士論文】
    （性病における非対称な異性間感染に関するSIRモデリング解析）
    
    
    In this paper, we considered the effect of the asymmetricity in the transmission dynamics of STDs on the population structure. The transmission rate and the newborn sex ratio appear to contribute fundamentally to the features of population structure with STDs. Indeed, the transmission rate could reflect the average number of sexual partners, the sexual activity, the physical natures, and so on. In this paper, we constructed our models to consider the contribution of the difference of population dynamical structure to the conclusion of STD dynamics. It is interestingly shown that the results are significantly different, depending on which female classes can contribute to the recruitment of newborns. Consequently, we have demonstrated that the sex ratio of infective population strongly depends on the dynamical structure of transmission of disease. Applying the incidence ratios from the statistical data of STDs in Japan, we consider the corresponding ratios for each of our models. As the result, we could suggest that those considered STDs have much asymmetric (biased) transmission rates, which were estimated to have not small order of difference. As for mathematical analysis along our modelling, we have still not a few open-problems to consider the general STDs. One of them is the effect of vertical transmission, in which mother's disease transmits to fetuses. Another is the mortality due to disease.
    

    発表：瀬野裕美，性病における非対称な異性間感染に関するSIRモデリング解析， 日本応用数理学会平成８年度年会オーガナイズド・セッション Demography and Epidemics，東京大学駒場キャンパス，1996年9月.
    
    Koide, C., Seno, H., 1996. Sex ratio features of two-group SIR model for asymmetric transmission of heterosexual disease, Mathl. Comput. Modelling, 23(4): 67-91.