【摘要】 研究一类具有非线性传染率且接触率系数受到白噪声干扰的随机SIRS流行病模型,证明了该模型正解的全局存在唯一性.通过构造Lyapunov函数讨论了模型解的渐近性态:当基本再生数小于1时,模型的无病平衡点是随机全局渐近稳定的;当基本再生数大于1时,随机系统的解围绕确定性模型的正平衡点振荡,且白噪声强度越高,振幅越大.最后,数值模拟结果验证了主要结论.更多还原

【Abstract】 A stochasic SIRS epidemic model with nonlinear incidence rate and white noise on incidence rate coefficient is investigated.By constructing Lyapunov function,the asymptotic behaviors of the model are discussed.The disease-free equilibrium of the model is stochastic global asymptotical stability when the basic reproduction number is less than one.The solution is fluctuate around the positive equilibrium of the deterministic model when the basic reproduction number is greater than one,and amplitude increases along with enhance of the noise intensity.Numerical simulations support the conclusions.更多还原