具非线性发病率随机SIQS传染病模型的渐近行为

The Asymptotic Behavior of a Stochastic SIQS Epidemic Model with Nonlinear Incidence

研究了一类具有非线性发病率的随机SIQS传染病模型,通过构造适当的Lyapunov函数并结合遍历论的相关结论,探讨该模型的解在其平衡点附近的动力学行为.研究结果表明:当R_0≤1时,随机模型的解会沿着无病平衡点(A/d,0,0)附近振动;当R_0>1时,该模型在地方病平衡点附近存在遍历的不变分布.

A general stochastic SIQS epidemic model with nonlinear incidence is investigated in this paper. By means of constructing appropriate Lyapunov functions and ergodicity theory, the asymptotically dynamical behaviors of a stochastic model around the positive equilibrium are considered. Our results show that if R0 ≤1, the solutions of the stochastic model fluctuate along the （A/d,0,0） and if R0≥1. the stochastic model admits an invariant distribution which is ergordic.