一类具有双线性发生率与常数治疗函数的SIRS传染病模型的动力学行为

摘要

The global dynamics of an SIRS epidemic model with bilinear incidence rate and constant treatment rate of infectious individuals are considered, and the effect of the treatment capacity on spread is studied in this paper. By mathematical analysis, it gives the sufficient conditions for the existence and asymptotic stability of the diseasefree and endemic equilibria. By numerical simulations, it is shown that the existence and stability of equilibria for the model is not only related to the basic reproduction number, but also related to the treatment capacity. At the same time it shows that when the endemic equilibrium is unstable, appropriate treatment can cure infectious diseases.%考虑了具有双线性发生率和常数治疗函数的SIRS 传染病模型的动力学行为，并且研究了治疗能力对传染病传播的影响。通过数学分析得到无病平衡点与地方病平衡点存在性和稳定性的充分性判据。数值模拟表明，模型平衡点的存在性与稳定性不仅与基本再生数有关，而且与治疗能力也密切相关。同时显示当地方病平衡点不稳定时，采用适当的治疗就能够根治传染病。