一种基于SEIS的封闭系统传染病模型

A Closed System Epidemic Model Based on SEIS

摘要: 本文针对一个封闭系统中的某种传染病进行研究，建立基于SEIS的感染病模型，讨论了系统中染病人数的变化情况。分析了潜伏者对传染病传播的影响，对于初始潜伏者是工作人员的情况和初始潜伏者是其他人员的情况分别讨论，调整模型参数，得到系统中人数变化图。接着分析了模型平衡点的稳定性，结果表明当R₀<1时，λ<0，平衡点A⁰是局部渐近稳定的；当R₀＞1时，λ＞0 故A⁰是不稳定的，存在地方性平衡点。我们还讨论了主要参数对感染人数的变化情况，结果表明传染率为影响染病人数的主要影响因素，其次是治愈率，因此发现传染病采取隔离，戴口罩等措施是十分必要的。

Abstract: This paper studies an infectious disease in a closed system, establishes an infectious disease model based on SEIS, and discusses the change of the number of infected people in the system. This paper analyzes the influence of the lurk on the spread of infectious diseases, discusses the situation that the initial lurk is a worker and the initial lurk is other people respectively, adjusts the model parameters, and obtains the change chart of the number of people in the system. Then the stability of the equilibrium point is analyzed. The results show that when R₀<1, λ<0, equilibrium point A⁰ is locally asymptotically stable; when  R₀＞1,  λ＞0, so A⁰ is unstable, and there is a local equilibrium point. We also discussed the changes of the main parameters on the number of infected people. The results show that the infection rate is the main factor affecting the number of infected people, followed by the cure rate. Therefore, it is necessary to isolate infectious diseases and wear masks.