Mathematical Theory of Structured Population Dynamics and its Applications

我们在这项研究中主要关注的是人口统计学，流行病学和理论生物学中的结构化人口模型的数学分析和模型开发。主要结果如下：[1]美洲锥虫病（美洲锥虫病）既可通过病媒传播，也可通过输血传播，具有急性短病程和慢性长病程的特点。我们已经制定了持续时间依赖的人口模型的恰加斯病和检查的存在性和稳定性的平衡状态。根据参数的取值，地方病稳态可能发生后向分支，这是预防策略中需要考虑的一个重要事实。[2]我们考虑一个年龄-持续时间-结构的同性恋社区HIV感染的人口模型。当基本再生产比大于1时，我们给出了后向或前向分岔发生的充分条件。我们给出了充分条件， ...更多信息 地方病平衡态的局部稳定性。[3]研究了一类具有年龄结构的SIR型传染病传播模型。证明了地方病平衡态存在的充要条件是基本再生比大于1，而无病平衡态是全局渐近稳定的，它小于1.我们还证明了当基本再生数超过1时，局部稳定的地方病稳定态是从无病稳定态向前分叉的。[4]研究了一类具有年龄结构的直接传染病传播的SIR流行病模型的数学结构，其中基本系统是无穷维齐次动力系统.考虑宿主种群由稳定种群模型描述的情况，证明了线性化稳定性原理，使得只要我们考虑基本系统的渐近行为，只要假设宿主种群已经达到稳定种群，就足以检验诱导的归一化系统.少

Our main concern in this research is mathematical analysis and model developments for structured population models in demography, epidemiology and theoretical biology. Main results are as follows:[1] Chagas disease (American trypanosomiasis) is transmitted by the vector population and also by blood transfusion and characterized by the existence of the acute short duration stage and the long chronic stage. We have formulated the duration-dependent population model for the Chagas disease and examined the existence and stability of the steady state. Depending on parameter values, the backward bifurcation of the endemic steady stat e can occur, which is an important fact to be considered in the preventive policy.[2] We consider an age-duration-structured population model for HIV infection in a homosexual community. W e have shown sufficient conditions for backward or forward bifurcation to occur when the basic reproduction ratio crosses the unity. We have given sufficient conditions for th … More e local stability of the endemic steady states.[3] We have considered a SIR type epidemic model for the spread of horizontally and vertically transmitted infectious diseases in an age-structured population. We proved that an endemic steady state exists if and only if the basic reproduction ratio is grater than unity, while the disease-free steady state is globally asymptotically stable it is less than unity. We also show that the locally stable endemic steady states are forwardly bifurcated from the disease-free steady state when the basic reproduction number crosses the unity.[4] We have studied mathematical structure of the SIR epidemic model for the spread of directly transmitted infectious diseases in age-structured host populations, in which the basic system is formulated as infinite-dimensional homogeneous dynamical systems. We consider the case that the host population is described by the stable population model and proved the linearized stability principle such that as far as we concern the asymptotic behavior of the basic system, it is sufficient to examine the normalized system induced by assuming that the host population has already attained the stable population. Less