一类具有治愈期和免疫失效期的SIRS模型  

The Stability and the Permanence of an SIRS Epidemic Model with Healing Period and Immune Expiration Period

作　　者：许立滨[1] 李冬梅[1] 杨美英[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2014年第6期113-117,共5页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅科学技术研究项目(12521099)

摘　　要：考虑具有治愈期和免疫失效期的离散双时滞的SIRS传染病模型,找到决定疾病灭绝与否的阈值,计算出模型的无病平衡点和地方病平衡点,证明了无病平衡点的全局稳定性.并利用反证法和比较原理,证明疾病的一致持久性.并通过数值模拟分析治愈期和恢复期对模型的影响.An SIRS epidemic model with two time delays in healing period and immune expiration period is re- searched. The threshold conditions which determines the epidemic termination were found out, the free-equilibrium and endemic equilibrium were calculated, and the global stability of free-equilibrium was proved. Using the method of rebuttal evidence and the comparison principle of differential equations, the uniform persistence of disease is proved. Immune expiration period and the recover period for the influence of epidemic model by numerical simula- tion were analyzed at last.

关 键 词：双时滞 治愈期 免疫失效期 稳定性 一致持久性 

分 类 号：O175[理学—数学]