数理生物学における力学系に関する総合的研究

2003 Fiscal Year Annual Research Report

• Project/Area Number: 13304006
• Research Institution: Shizuoka University
• Principal Investigator: 竹内 康博 静岡大学, 工学部, 教授 (20126783)
• Co-Investigator(Kenkyū-buntansha): 難波 利幸 大阪女子大学, 理学部, 教授 (30146956) ; 巌佐 庸 九州大学, 理学研究科, 教授 (70176535) ; 三村 昌泰 広島大学, 理学研究科, 教授 (50068128) ; 稲葉 寿 東京大学, 数理科学研究科, 助教授 (80282531) ; 古用 哲夫 島根大学, 総合理工学部, 教授 (40039128)
• Keywords: 数理生物学 / 力学系 / 微分方程式 / 時間遅れ / カオス / パーマネンス

Research Abstract

数理生物学で現れる代表的な力学系の諸性質を総合的に解析することが本研究の目的である.本年の研究実績の概要は以下のようにまとめられる.
(1)6月13日-23日カナダのアルバータ大学で開催された第4回バトラー記念会議参加し,海外共同研究者であるY.Kuang教授と共同研究.
(2)8月23日-28日と「Mathematics in Populationをイッキ読みする第2回合宿セミナー」を開催し「Mathematics in Population,(Princeton Series in Theoretical and Computational Biology)Horst R.Thieme(著)」,を26人の参加者でPartIIまで読破した.また数理生物学における力学系モデルの研究について交流をした,残されたPartIIIは本年5月末に行われる第3回イッキ読み合宿セミナーで読破される計画である.一昨年12月17-20日に行われた第1回合宿セミナーで用いられた「The Theory of the Chemostat : Dynamics of Microbial Competition (Cambridge Studies in Mathematical Biology),Hal L.Smith, Paul E.Waltman(著)」は本年2月に日本評論社から「微生物の力学系---ケモスタット理論を通して」として翻訳出版された.
(3)9月4日-17日数理生態学に関する第2回アルカーラ国際会議出席・発表並びに数理生物学における力学系モデルの共同研究.
(4)2月20日岡山大学環境理工学部で研究集会「環境と健康の数理生物学」を開催した.
(5)静大内の研究分担者を組織委員,静大外の研究分担者を科学委員として,静岡大学で国際シンポジウム
「Dynamical Systems Theory and Its Applications to Biology and Environmental Sciences:力学系理論と生物学・環境科学への応用」を3月14日-17日と開催した,シンポジウムでは数理生物学における力学系理論を数学と生物学の両側面から研究交流する目的であった.本シンポジウムは海外からの参加者50人を含め200人を超える参加者があった.特に日本の若手研究者の研究が多くの海外研究者から注目された.また海外共同研究者のE.Beretta教授とW.Ma教授も同シンポジウムに参加し,研究交流を行った.このシンポジウムにあわせて南京師範大学の崔教授は昨年10月から静岡大学に外国人研究者と滞在し,静大内の研究分担者と共同研究を行った.

Research Products

• [Publications] Y.Takeuchi, T.Yamamura: "Stability analysis of the Kaldor model with time delays : Monetary policy and government budget constraints"Nonl.Anal.Series B Real World Applications. 5・2. 277-308 (2004)
• [Publications] R.Kon, Y.Saito, Y.Takeuchi: "Permanence of single-species stage-structured model"J.Math.Biol.. (To appear).
• [Publications] R.Kon, Y.Takeuchi: "Permanence of 2-host,1-parasitoid systems"Dynamics of Continuous, Discrete and Impulsive Systems. Series B : Applications and Algorithms. 10. 389-402 (2003)
• [Publications] K.Tainaka, N.Yoshida, N.Terazawa, N.Nakagiri, Y.Takeuchi, J.Yoshimura: "The effect of mutualism on community stability and competitive interaction"J.Physics Soc.of Japan. 72・4. 956-961 (2003)
• [Publications] Y.Saito, Y.Takeuchi: "Sharp conditions for globa stability of Lotka-Volterra systems with delayed intraspecific competition"Fields Institute Communications. 36. 195-211 (2003)
• [Publications] W.Ma, Y.Takeuchi: "Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate"Discrete and Continuous Dynamical Systems-Series B. 4・3. 673-680 (2004)
• [Publications] M.Yamaguchi, Y.Takeuchi, W.Ma: "Population dynamics of sea bass and young sea bass"Discrete and Continuous Dynamical Systems-Series B. 4・3. 833-840 (2004)
• [Publications] H.Du, R.Kon, Y.Saito, Y.Takeuchi: "Dynamical behavior of Lotka-Volterra competition systems : non-autonomous bistable case and the effect of telegraph noises"J.Computational and Applied Mathematics. (To appear).
• [Publications] W.Ma, M.Song, Y.Takeuchi: "Global stability of an SIR epidemic model with time delay"Applied Math. Letters. (To appear).
• [Publications] J.Cui, Y.Takeuchi, Z.Lin: "Permanence and Extinction for Dispersal Population Systems"J.Math.Anal.Appl.. (To appear).
• [Publications] D.Hilhorst, M.Mimura, R.Schaetzle: "Vanishing latent heat limit in a Stefan-like problem arising in Biology"Nonlinear Analysis. 261-285 (2003)
• [Publications] E.Feiresl, D.Hilhorst, M.Mimura, R.Weidenfeld: "On a nonlinear diffusion system with resource-consumer interaction"Hiroshima Math.J.. 33. 253-295 (2003)
• [Publications] E.C.M.Crooks, E.N.Dancer, D.Hilhorst, M.Mimura, H.Ninomiya: "Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions"in Nonlinear Anal.Series B. (To apper).
• [Publications] H.Inaba, H.Sekine: "A mathematical model for Chagas disease with infection-age-dependent infectivity"Mathematical Biosciences. (To apper).
• [Publications] H.Inaba: "Backward bifurcation in a HIV/AIDS epidemic model with age structure I: The case of proportionate mixing (2003) 189-196"数理解析研究所講究録. 1309. 189-196 (2003)
• [Publications] H.Inaba: "Backward bifurcation in a model for vector transmission disease, In Morphogenesis and Pattern Formation in Biological Systems"T.Sekimura, S.Noji, N.Ueno, P.K.Maini (eds.), Springer. 271-279
• [Publications] H.Inaba: "Backward bifurcation in a HIV/AIDS epidemic model with age structure II: The case of general transmission rate"数理解析研究所講究録. 1337. 103-111 (2003)
• [Publications] 稲葉寿: "インフルエンザ流行-数理モデル"綜合臨牀. 52・10. 2700-2706 (2003)
• [Publications] Y.Itoh, K.Tainaka: "Extinction process and variation in a prey-predator system"J.Phys.Soc.Japan.. (To appear).
• [Publications] Y.Itoh, K.Tainaka, T.Sakata, T.Tao, N.Nakagiri: "Spatial Enhancement of Population Uncertainty near the Extinction Threshold"Ecological Modelling. (To appear).
• [Publications] N.Nakagiri, K.Tainaka: "Paradoxical effect in habitat destruction"Ecological Modelling. (To appear).
• [Publications] K.Tainaka: "Perturbation expansion and optimized death rate in a lattice ecosystem"Ecological Modelling. 163. 73-85 (2003)
• [Publications] 佐藤 一憲: "格子確率モデルの数理と応用:複雑性を有する確率モデルの数理的研究[VI・完]-生息地破壊の格子モデル-"電子情報通信学会誌. 86. 51-53 (2003)
• [Publications] S., Tohya, A.Mochizuki, Y.Iwasa: "Random cell rearrangement can form cone mosaic patterns in fish retina and explain the difference between zebrafish and medaka"J.Theor.Biology. 221. 289-300 (2003)
• [Publications] Michor, F., Y.Iwasa, N.L.Komarova, M.A.Nowak.: "Local regulation of homeostasis favors chromosomal instability"Current Biology. 13. 581-584 (2003)
• [Publications] Takano, R., A.Mochizuki, Y.Iwasa: "Possibility of tissue separation caused by cell adhesion"J.Theor.Biology. 221. 459-474 (2003)
• [Publications] Frank, S., Y.Iwasa, M.Nowak: "Pattern of cell division and the risk of cancer"Genetics. 163. 1527-1532 (2003)
• [Publications] H.Shoji, A.Mochizuki, Y.Iwasa, M.Hirata, T.Watanabe, S.Hioki, S.Kondo: "Origin of directionality in the fish stripe pattern"Developmental Dynamics. 226. 627-633 (2003)
• [Publications] Shudo, E., P.Haccou, Y.Iwasa: "Optimal choice between feedforward and feedback control in gene expression to cope with unpredictable danger"J.Theor.Biology. 223. 149-160 (2003)
• [Publications] Shoji, H, Y.Iwasa: "Pattern selection and the direction of stripes in two-dimensional Turing systems for skin pattern formation of fishes"Forma. 18. 3-18 (2003)
• [Publications] Yokomizo, H., J.Yamashita, Y.Iwasa: "Optimal conservation effort for a population in a stochastic environment"J.Theor.Biology. 220. 215-231 (2003)
• [Publications] Yokomizo, H., P.Haccou, Y.Iwasa: "Conservation effort for a population in a fluctuating environment and assessment of the population size"J.Theor.Biology. 224. 167-182 (2003)
• [Publications] Nakamaru, M., Y.Iwasa, J.Nakanishi: "Extinction risk to bird populations caused by DDT exposure"Chemosphere. 53. 377-387 (2003)
• [Publications] Nakanishi, J., M.Gamo, Y.Iwasa, Y.Tanaka: "Environmental Risk Evaluation of Chemicals: achievements of the project and seeds for future-Development of metrics for evaluating risks"Chemosphere. 53. 389-398 (2003)
• [Publications] Shoji, H., Y.Iwasa, S.Kondo: "Stripes, Spots or Reversed Spots in Two-dimensional Turing Systems"J.Theor.Biology. 224. 339-350 (2003)
• [Publications] Muko, S., Y.Iwasa: "Incomplete mixing promotes species coexistence in a lottery model with permanent spatial heterogeneity"Theoretical Population Biology. 64. 359-368 (2003)
• [Publications] Michor, F.M.A.Nowak, S.A.Frank, Y.Iwasa: "Stochastic elimination of cancer cells"Proceeding of Royal Society London ser.B.. 270. 2017-2024 (2003)
• [Publications] Michor F., S.A.Frank, R.M.May, Y.Iwasa, Nowak, M.A.: "Somatic selection for and against cancer"J.Theor.Biology. 225. 377-382 (2003)
• [Publications] Nowak, M.A., F.Michor, Y.Iwasa: "The linear process of somatic evolution"Proc.Nat.Acad.Sci.USA. 100. 14966-14969 (2003)
• [Publications] Iwasa Y., F.Michor, M.Nowak: "Evolutionary dynamics of escape from biomedical intervention"Proceeding of Royal Society London, ser B.. 270. 2573-2578 (2003)
• [Publications] Hakoyama, H., Y.Iwasa: "Coexistence of a sexual and a unisexual forms by parasites"Journal of Theoretical Biology. 226. 185-194 (2004)
• [Publications] Iwasa, Y., F.Michor, M.Nowak: "Evolutionary dynamics of invasion and escape"Journal of Theoretical Biology. 226. 205-214 (2004)
• [Publications] Satake, A., Y.Iwasa, H.Hakoyama, S.P.Hubbell: "Estimating local interaction from spatio-temporal forest data, and Mon te Carlo Bias Correction"Journal of Theoretical Biology. 226. 225-235 (2004)
• [Publications] Irie, T., Y.Iwasa: "Optimal growth model for the latitudinal cline of shell morphology in cowries (genus Cypraea)"Evolutionary Ecology Research. 5. 1133-1149 (2004)
• [Publications] Michor, F., Y.Iwasa, M.A.Nowak: "Dynamics of cancer progression"Nature Review Cancer. 4. 197-205 (2004)
• [Publications] Iwasa, Y., A.Satake: "Mechanisms inducing spatially extended synchrony in mast seeding : the role of pollen coupling and environmental fluctuation"Ecological Research. 19・1. 13-20 (2004)
• [Publications] Michor, F., Y.Iwasa, H.Rajagopalan, C.Lengauer, M.A.Nowak: "A linear model of colon cancer initiation"Cell Cycle. 3. 358-362 (2004)
• [Publications] Shudo, E., Y.Iwasa: "Dynamic optimization of defense, immune memory, and pathogens remaining in the host body"Journal of Theoretical Biology. (To appear).
• [Publications] Iwasa, Y., F.Michor, M.A.Nowak: "Stochastic tunnels in evolutionary dynamics"Genetics. (To appear).
• [Publications] T.Furumochi, S.Murakami, Y.Nagabuchi: "Stabilities in Volterra difference equations on a Banach space"Fields Institute Communications. (To appear).
• [Publications] T.Furumochi, S.Murakami, Y.Nagabuchi: "A generalization of Wiener's lemma and its application to Volterra dif ference equations on a Banach space"Journal of Difference Equations and Applications. (To appear).
• [Publications] T.Furumochi: "Asymptotic behavior of solutions of some functional differential equations by Schauder's theorem"E.J.Qualitative Theory of Differential Equations. (To appear).
• [Publications] T.A.Burton, T.Furumochi: "Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem"Nonlinear Studies. (To appear).
• [Publications] 福谷郁子, 重定南奈子, 高須夫悟: "リンデンマイヤー・システムとしての植物根系の形態"生物の形の多様性と進化-遺伝子から生態系まで-(関村・野馳,森田編),裳華房. 152-161 (2003)
• [Publications] Noriko Kinezaki, Kohkichi Kawasaki, Fugo Takasu, Nanako Shigesada: "Modeling Biological Invasions into Periodically Fragmented Environments"Theoretical Population Biology. 64. 291-302 (2003)
• [Publications] Nanako Shigesada, Noriko Kinezaki, Kohkichi Kawasaki, Fugo Takasu: "Biological Invasion into Periodically Fragmented Environments : Diffusion-Reaction Model"Morphogenesis and Pattern Formation in Biological Systems : Experiments and Models, Springer-Verlag Tokyo. 215-222 (2003)
• [Publications] Kyoko Ohsawa, Kohkichi Kawasaki, Fugo Takasu, Nanako Shigesada: "How does spatio-temporal disturbance influence species diversity in a hierarchical competitive system? Prospective order of species coexistence and extinction"Population Ecology. 45. 239-247 (2003)
• [Publications] M.Nakamaru, M.Kawata: "Evolution of rumors that discriminate lying defectors"Evolutionary Ecology Research. 6. 261-283 (2004)
• [Publications] M.Nakamaru, A.Sasaki: "Can transitive inference evolve in animals playing hawk-dove game?"Journal of Theoretical Biology. 222. 461-470 (2003)
• [Publications] T.Kajiwara, T.Sasaki: "Stability of pathogen-immune interaction"Discrete and Continuous Dynamical System Ser. B. (To appear).
• [Publications] Namba, T., Chon, T.-S.: "Mathematical view of community and ecosystem processes""Ecological Issues in a Changing World : Status, Response and Strategy", Kluwer Academic. (To appear).
• [Publications] 竹内康博(監訳): "微生物の力学系---ケモスタット理論を通して"日本評論社. 350 (2004)