具有饱和接触率的SIRS传染病模型的周期解

摘要

The dynamics of an SIRS epidemic model with birth pulse,pulse vaccination and saturation incidence is studied.The existence and stability of the trivial solution and infection-free periodic solution are analyzed.By using discrete mapping and bifurcation theory,the condition of occurrence for supercritical bifurcation is derived.The threshold for a disease to be extinct or endemic is established.Moreover,numerical results for phase portraits,periodic solutions and bifurcation diagrams are illustrated with an example,which are in agreement with the theoretical analysis.%基于离散映射和分岔理论,研究了具有脉冲生育、脉冲接种和饱和接触率的SIRS传染病模型的动力学性质,通过分析模型平凡解和无病周期解的存在性和稳定性以及超临界分岔发生的条件,得到决定疾病流行与否的阈值,给出验证理论分析的数值结果.