带有治疗项的SIS反应扩散传染病模型动力学分析

考虑了一类带有饱和治疗项的SIS反应扩散传染病模型。根据最小特征值得到疾病流行阈值——基本再生数,当基本再生数R01时,疾病的无病平衡点局部稳定;当R01时,无病平衡点不稳定且存在地方病平衡点。通过数值模拟,讨论了治疗项对疾病传播的影响。当疾病流行时,加强治愈率可以有效控制疾病的发展,然而扩大医院规模会促使疾病更大规模的流行。

A dynamics analysis of an SIS epidemic reaction-diffusion model with treatment

In this paper, we study the SIS epidemic reaction-diffusion model with the saturated treatment. We obtain the prevalence threshold value of disease, namely the basic reproduction number R₀, based on the least eigenvalue. We have proved that the unique disease-free equilibrium is local stable when R₀<1, while the disease-free equilibrium is unstable and the endemic equilibrium exists when R₀>1. Through numerical simulation, we discuss the influence of treatment on prevalence of disease. When disease outbreaks, it is efficient to increase cure rate for the control of the disease, while expanding the scale of hospitals will cause even more prevalence of the disease.