具有双时滞的SEIR疾病模型的Hopf分支分析  

Hopf Bifurcation Analysis in a SEIR Epidemic Model with two Delays

作　　者：于莉琦[1] 王强[2] 高恒嵩[1] 顾贞[1] 贺树立[1] 洪港[1] YU Liqi;WANG Qiang;GAO Heng-song;GU Zhen;HE Shu-li;HONG Gang(Mathematics Teaching and Research Section,East University of Heilongjiang,Harbin 150066,China;School of Computer,East University of Heilongjiang,Haxbin 150066,China)

机构地区：[1]黑龙江东方学院数学教研室,黑龙江哈尔滨150066 [2]黑龙江东方学院计算机学部,黑龙江哈尔滨150066

出　　处：《数学的实践与认识》2020年第21期305-313,共9页Mathematics in Practice and Theory

基　　金：黑龙江省自然科学基金(A2018006);黑龙江东方学院自然科学基金(HDFKY190128)。

摘　　要：研究既具有水平传染又具有垂直传染的SEIR疾病模型,并引入了两个时滞,分别为细胞因病毒引起感染的过程时滞和病毒在感染细胞内的繁殖时滞.讨论了该系统的正平衡点存在的条件,通过分析特征方程,建立了正平衡点的局部稳定性和以时滞为参数时Hopf分支的存在性.结果表明:两个时滞可能使正平衡点发生扰动,进而出现周期解,数值模拟验证了所得结论.Consider the dynamical behavior of a SEIR epidemic model with vertical transmission and two delays,namely the infection delay caused by free virus and the virus production delay.It is show that the existence of the positive equilibrium.By analyzing the characteristic equations,the local stability of the positive equilibrium and the existence of Hopf bifurcations when two delays are used as the bifurcation parameters are established.The results exhibit that both delays are able to destabilize the positive equilibrium and cause periodic solutions.Numerical simulations are carried to explain the mathematical conclusions.

关 键 词：SEIR疾病模型 时滞 局部稳定性 HOPF分支 

分 类 号：R51[医药卫生—内科学] O175[医药卫生—临床医学]