不连续治疗策略下的一类具有饱和发生率的SIR传染病模型

An SIR epidemic model with saturated incidence rate and discontinuous treatment

研究一类具有不连续治疗策略和饱和发生率的SIR传染病模型的动力学性态。利用右端不连续微分方程理论方法分析,得到模型在Filippov意义下解的存在性及无病平衡点和地方病平衡点的存在性。进一步得到,当R0≤1时,无病平衡点是全局渐近稳定的;当R0>1时,无病平衡点不稳定,地方病平衡点全局渐近稳定;证明在模型经过有限时间后,模型轨线收敛到无病平衡点。

The dynamical behaviors of an SIR model with saturated incidence rate and discontinuous treatment strategy are investigated. Firstly,the Filippov solution of the model is defined,and the existence of disease-free equilibrium and endemic equilibrium are obtained by using the theory of the differential equations with discontinuous right-hand side. Secondly,it is found that when R0≤1,the disease-free equilibrium is globally asymptotically stable; when R0 1,the disease-free equilibrium is not stable and the endemic equilibrium is globally asymptotically stable. In addition,it is shown that the model converge to the disease-free equilibrium point within a limited time.