具有脉冲出生与脉冲免疫不同时发生的SEIR传染病模型  

A SEIR Epidemic Model with Birth Pulse and Impulsive Vaccination at Different Moment

作　　者：周文[1] 侯高梅 连晓飞[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《南通大学学报（自然科学版）》2015年第3期65-72,94,共9页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11302002);安徽高校省级优秀青年人才基金重点项目(2011SQRL022ZD)

摘　　要：考虑染病者身体素质差异的因素,在脉冲出生与脉冲免疫不同时发生的条件下,建立了一类具有m类易感者群体的SEIR传染病模型,探索了预防控制传染病的理论途径.采用频闪映射计算无病周期解,并利用比较定理研究疾病流行与否的充分条件.计算结果表明:R1<1时,疾病消失;R2>1时,疾病持久存在.观察临界值R1,R2,当k=1时,即脉冲出生点处进行脉冲接种将更有利于疾病的控制.With the different physical quality causing different susceptibility for disease, the susceptibles were divided into m class groups. Because birth pulse and impulsive vaccination occur at different moment and supposing some newborns have innate immunity against diseases, the theoretical methods on controlling and prevention the disease was investigated. With the help pf the discrete dynamical system determined by the stroboscopic map, the exact ex- pression of infection-free periodic solution was calculated. By the comparison theorem of impulsive equation, the conditions of global attractivity of infection-free periodic solution and permanence were obtained. Facilitated by the stroboscopic map and the comparison theorem of impulsive equation, the existence of infection-free solution was proved. The conditions of global attractivity of infection-free periodic solution and permanence were also derived. It was found that that when k = 1, it is of benefit to treat diseases by relationship between the critical value and k. Fur- thermore isolation treatment is a good way to control the spread of the disease.

关 键 词：脉冲出生 脉冲免疫 SEIR传染病模型 

分 类 号：O193[理学—数学]