带有非线性发生率的离散SIR模型的动力学行为

Analysis of dynamics behavior of the discrete SIR model with a nonlinear incidence rate

摘要:

本文探究了带有非线性发生率λSpI的离散SIR传染病模型的动力学行为. 本文首先确定了无平衡点的拓扑类型, 包括平衡点的存在性和稳定性，然后进一步地分析了无病平衡点的分岔情况.通过中心流行定理和正规型理论, 本文发现了限制在系统中心流行上的flip分岔以及NeimarkSacker分岔, 给出了各自的分岔方向.最后,对所得的数学结果给出了相应的生物学解释.

Abstract:

In this paper we investigate the dynamics behavior of the discretetime SIR epidemic model with a nonlinear incidence rate λSpI. Firstly, we determine the topological type of the endemic fixed point, including the existence and stability of the fixed point. Furthermore, we analyze the bifurcation situations, and discuss the flip bifurcation on the center manifold and the NeimarkSacker bifurcation of this SIR system by center manifold theorem and normal form theory. Their bifurcation directions are given respectively. Finally, some biological explanations of our mathematical results are presented.