The Dynamic Properties of a Deterministic SIR Epidemic Model in Discrete-Time

• 作者: Hongbo Wang Wenbo Zeng Xiaodan Liao Xiaohua Huang Xiaoliang Zhou
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: EPIDEMIC Model Equilibrium Point TRANSCRITICAL Bifurcation Center MANIFOLD HYPERBOLICITY
• 年，卷（期）: 2015,（10）
• 页码范围: 1665-1675
• 页数: 11页
• 分类号: O1

摘要

In this paper, a class of discrete deterministic SIR epidemic model with vertical and horizontal transmission is studied. Based on the population assumed to be a constant size, we transform the discrete SIR epidemic model into a planar map. Then we find out its equilibrium points and eigenvalues. From discussing the influence of the coefficient parameters effected on the eigenvalues, we give the hyperbolicity of equilibrium points and determine which point is saddle, node or focus as well as their stability. Further, by deriving equations describing flows on the center manifolds, we discuss the transcritical bifurcation at the non-hyperbolic equilibrium point. Finally, we give some numerical simulation examples for illustrating the theoretical analysis and the biological explanation of our theorem.