一类非线性脉冲免疫接种SIR传染病模型的周期解与分支

由于受到医疗资源的限制,疫苗的免疫接种率一般不是常数。采用非线性脉冲免疫接种函数,建立了一类具有终身免疫的脉冲预防接种SIR模型,利用频闪映射及差分方程的不动点,讨论了模型无病周期解的存在性;运用Floquet乘子理论和脉冲微分方程比较定理,证明了模型无病周期解的全局渐近稳定性;选取脉冲免疫接种周期为分支参数,利用分支定理,给出了系统存在正周期解的充分条件。

Periodic Solution and Bifurcation of an SIR Epidemic Model with Nonlinear Pulse Vaccination

Due to limited medical resources, vaccine immunization rates are not often constant. To adapt nonlinear pulse vaccination function, an SIR epidemic model with lifelong immunity and pulse vaccination is stablished. By using stroboscopic map and fixed point of difference equations, the existence of disease free periodic solution in the model is discussed. The global asymptotically stability of disease free periodic solution is proved by applying Floquet multiplier theory and differential pulse comparison theorem. By choosing the pulse vaccination period as a bifurcation parameter, a sufficient condition under which the system has a positive periodic solution is obtained by using the bifurcation theorem.