非连续策略对具有非线性发生率的SIRS模型的影响

Impact of Discontinuous Treatments on Disease Dynamics in a SIRS Epidemic Model With a Nonlinear Incidence Rate

该文提出了一个具有非连续治疗策略和非线性发生率的SIRS模型.在合理的猜想之下,我们定义了模型的基本再生数R0,并利用微分包含的相关知识来研究该SIRS模型平衡点存在性问题.当R0>1时,通过构造相应的Lyapunov函数可证明模型满足初始条件的每一个解都在有限时间内全局收敛于地方平衡点;当R0<1时,同样研究了模型在有限时间内的全局收敛性.所得结果改进和拓展了文献中的相应结果.

A SIRS epidemic model with discontinuous treatment and nonlinear incidence rate is proposed in this paper. Under some reasonable suggestion, we get the basic reproduction number of this model. Moreover, it has proved the existence of equilibrium by using the knowledge of differential inclusion. If R0 〉 1,we bui ld a corresponding Lyapunov function and achieve the convergence to the endemic equilibrium in finite time; If R0 〈 1,we also prove the convergence to the disease free equilibrium in finite time. The results of references are improved and extended.