一类具有时滞和进化效应的SIR模型的稳定性和Hopf分支分析

Stability and Hopf bifurcation analysis of the SIR model with time-delay and evolutionary effects

本文主要研究了一类在齐次Neumann边界条件下具有时滞和进化效应的SIR模型.首先,以时滞为参数,分析了时滞对该系统正平衡点稳定性的影响,并给出了Hopf分支的存在条件.其次,利用规范型理论和中心流形定理,得到Hopf分支方向和分支周期解的稳定性.最后,利用Matlab进行数值模拟,验证结论的正确性,得出时滞会使稳定的系统变得不稳定,并产生Hopf分支.

In this paper,we study a class of SIR model with time-delay and evolutionary effects under the homogeneous Neumann boundary conditions.Firstly,the stability of the positive equilibrium point is analyzed with time delay as the parameter,and the existence condition of Hopf bifurcation is given.Secondly,the bifurcation direction and the stability of periodic solutions are given by using the theory of normal form and center manifold.Finally,Matlab was used for the numerical simulation to verify the correctness of the conclusion,and it is concluded that the time delay will make the stable system become unstable and generate Hopf bifurcation.