一类具有连续接种的时滞SEIR传染病模型  

The Delayed SEIR Epidemic Model with Continuous Vaccination

作　　者：朱焕[1,2] 李冬梅[2] 刘伟华[2] 袁玉萍[1] 

机构地区：[1]黑龙江八一农垦大学理学院 [2]哈尔滨理工大学应用科学学院

出　　处：《哈尔滨理工大学学报》2013年第5期123-128,共6页Journal of Harbin University of Science and Technology

基　　金：黑龙江省自然科学基金(A200502);黑龙江省教育厅科学技术研究项目(12521099);大庆市科技局项目(szd201126);教育部博导类课题资助项目(20112305110002)

摘　　要：针对具有预防接种且疫苗具有一定有效期,总人口在变化的SEIR传染病模型,以有效接触率β为参数,对模型进行了Hopf分支存在性分析,指出当接触率β较小时,系统正平衡点仍保持稳定性,而当β经过一临界值β0后,系统正平衡点的稳定性发生改变,并在此临界处产生Hopf分支.进一步,利用中心流形理论和规范型方法得到了Hopf分支周期解的分支方向和稳定性的条件.A kind of SEIRS epidemic model with valid term is investigated. By choosing the effective contact rate as the parameter, the existence of the Hopf bifurcation is analyzed, and the phenomenon that the positive equi- librium is still keeping stable when the effective contact rate/3 is small but the stability will be destroyed while the effective contact rate processes a critical point and Hopf bifurcation appears at this point is indicated. Finally, the explicit formulates to determine the stability and direction of bifurcating period solutions are deduced by using the center manifold and the normal form theories.

关 键 词：预防接种 疫苗有效期 传染病模型 HOPF分支 分支方向 

分 类 号：O175.1[理学—数学]