几乎周期反应扩散传染病模型的动力学行为研究

项目名称： 几乎周期反应扩散传染病模型的动力学行为研究

项目编号： No.11501269

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 王宾国

作者单位： 兰州大学

项目金额： 18万元

中文摘要： 传染病的预防和控制是当前世界各个国家所面临的重要的公共卫生问题之一。传染病的爆发是多种因素混合作用的结果，其中个体随机运动导致的空间扩散和时空的非齐次性是影响疾病传播的重要因素。反应扩散方程经常被用来描述种群的移动和空间结构。时间的非齐次是季节性因素引起的，而季节性往往用周期性来反映。几乎周期函数作为周期函数的一般化，能更一般地揭示各种季节性因素在疾病传播中的交互影响作用。本项目主要借助（单调）动力系统，非线性泛函，遍历等理论在空间区域有界和无界的假设下，研究几乎周期反应扩散传染病模型的动力学行为。在此，我们将建立几乎周期反应扩散传染病模型的基本再生数的定义及其相关理论和计算公式，计算极小波速，找到几乎周期行波存在的条件，从而获得传染病持久和消亡的阈值参数。作为应用，结合年龄结构和潜伏期等因素，将考虑当前常见的传染病模型的基本再生数，流行波及传播速度，为疾病的控制和预防提供策略。

中文关键词： 基本再生数；几乎周期；反应扩散；传染病模型；极小波速

英文摘要： Prevention and control of infectious diseases are one of the important public health issues for all countries of the world. A mixing factors lead to the outbreaks of infectious disease. Spatial and temporal heterogeneity are most important factors. We use reaction-diffusion systems to represent the movements of populations and spatial structures. Seasonality induces the temporal heterogeneity. As a generalization of periodic functions, almost periodic functions represent accurately the impact of the seasonality in the spread of infectious disease. In this projector, we study the dynamics of almost periodic reaction-diffusion epidemic models by means of (monotone) dynamical system, nonlinear functional analysis and ergodic theory, and establish the theory of the basic reproduction ratio and its computation formulae, minimal wave speed, and find the condition of the existence of almost periodic traveling wave for almost periodic epidemic models. Furthermore, we also apply the developed theory to obtain a threshold type result for uniform persistence and global extinction of the disease. As applications, we consider the dynamics of some realistic epidemic models and some models with age structure or incubation period to provide a policy for the prevention and control of a disease.

英文关键词： Basic reproduction numbers;Almost periodicity;Reaction-Diffusion ;Epidemic models;Minimal wave speed