时滞传染病模型的稳定性与分支分析

Stability and Bifurcation Analysis of Epidemic Model with Time Delay

研究时滞传染病模型.从对模型线性化方程的特征方程根的分布分析入手,讨论了模型正平衡点的局部稳定性,确定了模型的线性稳定性区域,发现当模型中的时滞经过一系列临界值时,模型经历了Hopf分支和Hopf-Zero分支.最后,数值模拟验证了理论结果.

The epidemic model with time delay is studied. By analyzing the characteristic equation of the linearized system of original system,we obtain the local stability of the positive equilibrium,and establish the regions of linear stability of the equilibria. It is found that the model undergo the Hopf bifurcation and Hopf- Zero bifurcation when the delay passes through a sequence of critical values. Finally,some numerical simulations are carried out to support the analytic results.