一类基于心理作用的随机SIRS传染病模型

A Class of Stochastic SIRS Epidemic Model Based on Psychological Effect

首先建立了一类基于心理作用的随机SIRS传染病模型,通过构造Lyapunov函数,利用Ito引理,强大数定理和停时等随机分析理论,证明了模型全局正解的存在唯一性,并给出使疾病灭绝或持久的充分条件.其次,考虑了时滞对系统的影响,证明了基于心理作用的时滞随机SIRS传染病模型全局正解的存在唯一性.最后,应用Euler方法和Milstein方法进行数值模拟,验证本文建立的结论.

The paper considers a class of stochastic SIRS epidemic models based on psychological effects.By constructing Lyapunov functions,using the Ito lemma,the strong law of large numbers theorem and the stopping time and other stochastic analysis theories,the existence and uniqueness of the global positive solution of the model is established.And sufficient conditions are given to make the disease extinct.Besides,the persistence of the disease is studied in this paper.Based on such models,the effect of time delay on the system is considered,and the existence and uniqueness of the global positive solution of the stochastic SIRS epidemic model with psychological effect and time delay is established.Finally,numerical simulations including the Euler method and the Milstein method are used to verify the conclusions established in this paper.