具有群体作用机制和生灭效应的扩散SIS流行病模型：分析、模拟及与其他机制的比较
On a diffusive SIS epidemic model with mass action mechanism and birth-death effect: Analysis, simulations and comparison with other mechanisms
摘要：
本文研究了一类具有质量作用传染机制和线性生灭增长的SIS传染病反应扩散模型。通过定性分析，研究了均匀环境中无病平衡点的稳定性、关于基本再生数的一致持久性和地方病平衡点的全局稳定性，以及非均匀环境中当易感种群和感染种群的移动速率之一较小时，地方病平衡点（当存在时）的渐近分布.我们的研究结果，以及在其他三个密切相关的模型系统的工作，表明因素，如感染机制，总人口的变化和人口流动中发挥重要的，但微妙的作用，疾病的传播动力学，从而提供了有益的见解疾病控制和预防的策略设计。
英文摘要：
In the present paper, we are concerned with an SIS epidemic reaction-diffusion model governed by mass action infection mechanism and linear birth-death growth with no flux boundary condition. By performing qualitative analysis, we study the stability of the disease-free equilibrium, uniform persistence property in terms of the basic reproduction number and the global stability of the endemic equilibrium in homogeneous environment, and investigate the asymptotic profile of endemic equilibria (when exist) in heterogeneous environment as one of the movement rate of the susceptible and infected populations is small. Our results, together with those in previous works on three other closely related modeling systems, suggest that the factors such as infection mechanism, variation of total population and population movement play vital but subtle roles in the transmission dynamics of diseases and hence provide useful insights into the strategies designed for disease control and prevention.
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