一类质量作用感染机制下的SIS反应扩散移流模型
发布时间：2019-01-05 04:33
【摘要】：在理论流行病学中,SIS (易感者-染病者-易感者)模型提供了研究疾病传播动力学的基本框架.为研究环境的非齐次性和种群运动对疾病持续和灭亡的影响,我们研究一类具有零流边界条件的SIS反应扩散移流模型,这里我们考虑了易感者的出生率和死亡率以及染病者的死亡率,因此该模型的总人口数可能是不恒定的.首先,本文研究当易感者的出生率和死亡率相等,且染病者的死亡率为零时的SIS传染病模型.我们给出此时的基本再生数R_0的定义,它在决定疾病持续还是灭亡时起到关键作用.结果表明:当R_0 1时,无病平衡解是唯一和全局渐近稳定的;当R_0 1时,无病平衡解不稳定.当易感者的扩散速率和染病者的扩散速率相等时,结果显示:当R_0≤ 1时,无病平衡解是全局稳定的;而当R_0 1时,地方病平衡解是全局稳定的.其次,本文着重考虑了易感者的出生率大于易感者的死亡率,染病者的死亡率为正的情况.本文利用分支理论证明了平衡解的存在性.另外,在一种特殊情形下,本文运用上下解方法对平衡解进行估计.结果表明:当初值满足一定条件时,易感者的数目最终会保持有界,而染病者的数目会是一个无界值.
[Abstract]:In theoretical epidemiology, the, SIS (susceptible-infected-susceptible) model provides a basic framework for studying the dynamics of disease transmission. In order to study the inhomogeneity of environment and the effect of population movement on the persistence and extinction of disease, we study a SIS reaction-diffusion model with zero flow boundary condition. Here we consider the birth rate and death rate of the susceptible and the death rate of the infected, so the total population of the model may not be constant. First of all, this paper studies the SIS infectious disease model in which the birth rate and death rate are equal and the mortality rate of infected persons is 00:00. We give the definition of the basic regenerative number R _ S _ 0, which plays a key role in determining whether the disease continues or dies. The results show that the disease-free equilibrium solution is unique and globally asymptotically stable when R _ S _ (0.1) and R _ S _ (0.1) are unstable. When the diffusion rate of susceptible person is equal to that of infected person, the results show that the disease-free equilibrium solution is globally stable when R _ S _ 0 鈮，
本文编号：2401274
[Abstract]:In theoretical epidemiology, the, SIS (susceptible-infected-susceptible) model provides a basic framework for studying the dynamics of disease transmission. In order to study the inhomogeneity of environment and the effect of population movement on the persistence and extinction of disease, we study a SIS reaction-diffusion model with zero flow boundary condition. Here we consider the birth rate and death rate of the susceptible and the death rate of the infected, so the total population of the model may not be constant. First of all, this paper studies the SIS infectious disease model in which the birth rate and death rate are equal and the mortality rate of infected persons is 00:00. We give the definition of the basic regenerative number R _ S _ 0, which plays a key role in determining whether the disease continues or dies. The results show that the disease-free equilibrium solution is unique and globally asymptotically stable when R _ S _ (0.1) and R _ S _ (0.1) are unstable. When the diffusion rate of susceptible person is equal to that of infected person, the results show that the disease-free equilibrium solution is globally stable when R _ S _ 0 鈮，
本文编号：2401274
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