具有随机干扰和脉冲效应的SIS传染病模型的动力学分析  

Dynamic behaviors of an SIS epidemic model with random disturbance and impulsive effect

作　　者：林娇[1] 蒋贵荣[1] 刘苏雨[1] 龙腾飞[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2014年第6期509-513,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11162004);广西自然科学基金(2012GXNSFAA053006);广西研究生教育创新计划(YCSZ2014143);桂林电子科技大学研究生教育创新计划(GDYCSZ201472)

摘　　要：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。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.

关 键 词：SIS传染病模型 脉冲效应 随机扰动 随机指数渐近稳定 

分 类 号：O175.1[理学—数学]