一类具有非线性发生率的随机SIRS传染病模型的动力学行为

Dynamics Behavior for a Class of Stochastic SIRS Epidemic Model with General Nonlinear Incidence

研究一类具有非线性发生率的随机SIRS传染病模型,定义了新的随机基本再生数.通过构造Lyapunov函数,运用伊藤公式,建立了无病平衡点全局稳定性、疾病平均持续性的阈值判别准则.探讨环境变化对疾病的影响,结果表明白噪声强度在一定条件下会抑制疾病的爆发.

A class of stochastic SIRS epidemic models with general nonlinear incidence is investigated.The random basic reproductive number is identified.By constructing suitable Lyapunov function and applying Ito formula,the existence of unique global positive solution with any positive initial value is established.The influence of disease is also discussed when the environment changes.The results show that the intensity of white noise suppresses the outbreak of the disease under certain condition.