一类具有脉冲接种与脉冲剔除的SIQR模型

An SIQR mode with impulsive vaccination and impulsive elimination

同时考虑了脉冲接种、脉冲剔除和隔离策略,建立了一个SIQR传染病模型,从理论分析和数值模拟方面研究了SIQR传染病模型的动力学性质.首先,得到了模型的无病周期T解的存在性和基本再生数R0;其次,应用Floquet定理证明了无病周期T解的局部渐近稳定性和利用脉冲微分不等式证明了其全局渐近稳定性;接着,进行了计算机数值模拟来进一步验证理论结果的正确性.最后,通过对基本再生数R0及其偏导数,分析了脉冲接种、脉冲剔除和隔离这些预防和控制策略对传染病流行的影响.

Impulsive vaccination,impulsive elimination and quarantine strategies were considered in an SIQR epidemic model.The dynamical behavior of an SIQR epidemic model was discussed both theoretically and numerically.Firstly,the disease-free T periodic solution and the basic reproductive number R0 were obtained.Secondly,the local asymptotic stability of the disease-free T periodic solution with Floquet theorem was proved and the global asymptotic stability of the disease-free T periodic solution was also proved by impulsive differential equation.Thirdly,numerical simulation was conducted to illustrate the theoretical analysis.Finally,the influence of impulsive vaccination,impulsive elimination and quarantine strategies for epidemics was analyzed by the expression of the basic reproductive number R0 and its partial derivative.