一类有限资源下的非光滑传染病模型

A non-smooth epidemic model with limited resources

目的研究有限医疗资源对接种策略及传染病预防控制的影响。方法引入阈值控制策略到经典传染病模型中,建立非光滑传染病模型,刻画如下具有阈值水平的接种策略:当易感人数超过阈值水平时,实施常数接种策略,否则实施与易感人数成正比的接种策略。在子系统动力学研究的基础上,对非光滑系统进行研究。结果得到了非光滑系统规则平衡态和广义平衡态的稳定性。结论当疾病不能清除时,选取适当的控制参数可使染病人数最终控制在给定水平。

Purposes—To investigate the impact of limited medical resources on the vaccination strategy as well as the control outcome of epidemic disease.Methods—A non-smooth epidemic model is proposed by introducing the threshold policy into the classic epidemic model.It is used to describe the vaccination policy,i.e.the constant vaccination strategy is implemented once the number of susceptible individuals is above the threshold level.Otherwise,the policy proportional to the number of susceptible is adopted.The dynamical behavior of the formulated system is examined based on the dynamics of the subsystems.Results—The stability of the regular equilibria and generalized equilibria is addressed.Conclusion—The number of infected individuals can be contained at the previously given level by choosing a set of proper control parameter if the disease cannot be eradicated.