一类病毒自身发生变异的随机传染病SIS模型全局正解的渐近行为  

Asymptotic behavior of global positive solution to a stochastic SIS epidemic model with virus auto variation

作　　者：姬文鹏[1] 张天四[1] 徐丽筱[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《山东大学学报（理学版）》2013年第5期105-110,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11126097)

摘　　要：考虑了一类恢复率受到影响,且病毒自身发生变异的随机传染病模SIS型。研究了解的存在惟一性和有界性,证明了当基本再生数max{R1,R2}≤1时无病平衡点的随机渐近稳定性,并指出在噪声σ1足够大时,病毒可趋于灭绝的结论。最后通过数值仿真验证了本结论。This paper considers a stochastic SIS epidemic model with virus auto variation,in which the recovery rate is influenced by white noise.First,we prove the global existence,uniqueness of the positive solution,and show that the disease-free equilibrium is stochastically asymptotical stability when max{R1,R2}≤1.Then we point out when the white noise σ1 is large enough,the virus tends to disappear.Finally,the numerical simulations are carried out to support our results.

关 键 词：随机传染病SIS模型 LYAPUNOV函数 Ito^公式 渐近行为 

分 类 号：O175.1[理学—数学]