传染病的SI微分方程模型及稳定性分析

The SI Differential Equation Model of Epidemics and Its Analysis of Stability

利用微分方程的基本知识和疾病传播的一般规律及人口守恒统计法则建立起SI与SIR的传染病模型,再运用微分方程定性理论的数学方法,重点对SI的传染病模型进行定性与稳定性分析,从而得出相应情况下的生态意义。

This paper introduces a method to establish the SI epidemical model and SIR epidemical model with the basic knowledge of differential equations, the general rules of epidemic spreading and statistical rules of population conservation. Applying the qualitative theory of differential equations, the qualitative analysis and stability analysis of the SI epidemical modal can be done. Therefore, the ecological significance under different situations is obtained.