带有时滞的双传染病假设模型稳定性及Hopf分岔分析

Analysis on Stability and Hopf Bifurcation in a Delayed Epidemic Model with Double Epidemic Hypothesis

摘要: 本文主要分析带有时滞影响下的双传染病假设模型的稳定性及Hopf分岔，研究了不同情况下的系统唯一的正平衡点的稳定性，并通过分析相应线性系统的特征根的分布，得到了使得系统平衡的条件。然而，当时滞的值通过一个临界值的时候，Hopf分岔就会发生。最后, 运用MATLAB数值模拟去验证得到的理论结果。

Abstract: This paper mainly investigates the stability and Hopf bifurcation in a delayed epidemic model system with double epidemic hypothesis. We study the stability of the unique positive equilibrium for the system under different conditions. By analyzing the distribution of characteristic roots of corresponding linearized system, we obtain the conditions for keeping the system to be stable. Moreover, it is illustrated that the Hopf bifurcation will occur when the delay passes through a criti-cal value. Then we use the MATLAB numerical simulations for justifying the theoretical results.