一类具有信息干预和非线性函数的随机SIRS模型性质研究

A Study on the Properties of a Stochastic SIRS Model with Information Intervention and Nonlinear Incidence Rate

课题组研究了一类具有信息干预和非线性发生率函数的随机SIRS模型的渐近性质,先利用随机微分方程理论构造了恰当的Lyapunov函数,获得了模型灭绝性和持久性的充分条件;再通过数值模拟来验证,结果表明:被感染者的随机噪声扰动有利于抑制流行病的爆发。

The asymptotic properties of a class of stochastic SIRS model with information intervention and nonlinear incidence function are studied.Firstly,by using the theory of stochastic differential equations,appropriate Lyapunov functions are constructed to obtain sufficient conditions for the extinction and persistence of the model;then numerical simulations are conducted to verify the obtained results.The research indicates that the stochastic perturbation of infected individuals is beneficial for suppressing the outbreak of epidemics.