一类具时滞的传染病模型的建模及动力学性质分析——以新型冠状病毒感染为例

Mathematical Modeling and Dynamic Analysis of an Infectious Disease Model With Delay: A Case Study of Novel Coronavirus Infection

基于SEIR传染病模型,考虑到新型冠状病毒感染具有潜伏期的特性,建立了以潜伏期为时滞参数的泛函微分方程。首先,分析改进后的SEIR传染病模型的平衡点的存在性与稳定性;然后,分析Hopf分支的存在性与时滞参数的变化对于系统稳定性的影响;最后,利用MATLAB数值模拟验证结论的正确性。

Based on the SEIR infectious disease model, considering the incubation period of novel coronavirus infection, a functional differential equation with incubation period as a time delay parameter was established. Firstly, the existence and stability of the equilibrium point of the improved SEIR infectious disease model were analyzed. Then, the influence of the existence of Hopf branch and the change of time delay parameters on system stability was analyzed. Finally, the correctness of the conclusions was verified by MATLAB numerical simulation, and the analysis and suggestions for epidemic prevention and control were given through the results of numerical simulation.