College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China.
School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China.
Comput Math Methods Med. 2021 Jul 1;2021:1895764. doi: 10.1155/2021/1895764. eCollection 2021.
Epidemic models are normally used to describe the spread of infectious diseases. In this paper, we will discuss an epidemic model with time delay. Firstly, the existence of the positive fixed point is proven; and then, the stability and Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equations. Thirdly, the theory of normal form and manifold is used to drive an explicit algorithm for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions. Finally, some simulation results are carried out to validate our theoretic analysis.
流行病模型通常用于描述传染病的传播。在本文中，我们将讨论一个具有时滞的流行病模型。首先，证明了正平衡点的存在性；然后，通过分析相关特征方程根的分布，研究了稳定性和 Hopf 分支。第三，利用正规形和流形理论，给出了确定 Hopf 分支方向和分支周期解稳定性的显式算法。最后，进行了一些数值模拟来验证我们的理论分析。
