具有随机干扰和脉冲效应的SIS传染病模型的动力学分析

摘要

By using the comparison theorem of stochastic differential equation,Ito formula and Lyapunov exponent of stochas-tic nonlinear theory,an SIS epidemic model with impulsive effect and random disturbance is investigated.The existence of the positive solution and the infection-free solution are analyzed,and the sufficient condition for the existence of stochastic exponential asymptotic stable trivial solution is obtained.Moreover,numerical results which are illustrated with an exam-ple,are in good agreement with the theoretical analysis.%借助随机微分方程的比较定理、伊藤公式和随机非线性理论中的 Lyapunov指数，研究一类具有脉冲效应和随机干扰的 SIS传染病模型，分析模型的正解和无病解的存在性，得到了平凡解的随机指数渐近稳定的充分条件。数值模拟验证了理论分析的合理性。