具有垂直传染的随机SIR传染病模型的定性分析

Qualitative Analysis of Stochastic SIR Epidemic Model with Vertical Infection

考虑易感体、染病体的死亡率受环境因素的影响,在一类具有垂直感染的SIR传染病模型的基础上,加入随机干扰,建立一类具有垂直感染的随机SIR传染病模型。通过建立合理的Lyapunov函数,结合Ito积分,给出该系统依期望全局渐近稳定的判别准则,并利用Matlab软件进行数值仿真,阐明所建理论的准确性与有效性。

Based on the SIR infectious disease model with vertically infection,considering that the mortality rates of susceptible and infected bodies were affected by environmental factors,a class of stochastic SIR epidemic model with vertical infection was established.By establishing a reasonable Lyapunov function and combining with Itôintegral,the criterion of the expected global asymptotic stability of the system was given.The accuracy and effectiveness of the established theory were demonstrated by numerical simulation with Matlab software.