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A study for mathematical theory and applications of structured population dynamics

结构种群动态数学理论与应用研究

基本信息

批准号：
12640105
负责人：
INABA Hisashi
金额：
$ 2.18万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

(l) We have developed a two-sex age-structured population model with homogeneous marriage function as an evolution equation system and constructed its semigroup solution. Existence of persistent solution (exponential solution) has been proved for general marriage function.(2) We have formulated a nonlinear age-structured population model for marine invertebrates with density dependent mortality. We have constructed a positive semigroup solution, and proved the sufficient condition for the stability of the steady state solution. We have also the possibility of unstable steady state solution and oscillatory behavior.(3) We have formulated an epidemic model for type A influenza that takes into account the evolutionary aspects of virus, and examined it as an evolutionary equation. We have established the threshold condition for disease invasion and existence of endemic steady state. The possibility of unstable endemic steady state has been Oalso shown.(4) We have constructed a duration-dependent epidemic model for vector transmitted diseases like as Chagas disease, and shown that a backward bifurcation of endemic steady states can occur if there exists a disease-induced death rate.(5) We have formulated and analyzed an age-duration-structured population model for HIV infection in homogeneous community. We have established the threshold condition for invasion and existence of endemic steady states. It was also shown that a backward bifurcation of endemic steady slates can occur, so multiple endemic steady states are possible.(6) We have analyzed the behavior of a pair formation model for sexually transmitted diseases with subpopulations divided by sexual activity. And we have constructed an individual-based model to simulate sexually transmitted diseases.

(L)建立了一个具有齐次婚姻函数的两性年龄结构人口模型作为发展方程组，并构造了它的半群解。证明了一般婚姻函数的持久解(指数解)的存在性。(2)建立了具有密度依赖死亡率的非线性年龄结构海洋无脊椎动物种群模型。构造了一个正半群解，并证明了定态解稳定的充分条件。我们还存在不稳定的稳态解和振荡行为的可能性。(3)我们建立了一个考虑了病毒进化方面的甲型流感流行病模型，并将其作为进化方程进行了检验。我们已经建立了疾病侵袭和存在地方病稳态的阈值条件。(4)建立了恰加斯病等媒介传播疾病的持续时间相关的流行病模型，证明了如果存在疾病致死率，则可能发生地方病稳态的后向分叉。(5)建立并分析了同质社区HIV感染的年龄-持续时间结构的种群模型。我们已经建立了地方病稳态入侵和存在的阈值条件。研究还表明，地方性传播疾病的稳态可能出现向后分叉，因此可能存在多个地方性传播的稳态。(6)我们分析了对子种群按性行为划分的性传播疾病配对形成模型的行为。我们还构建了一个基于个体的模型来模拟性传播疾病。