Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity

Abstract EN

SIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed.

Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function.

Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem.

Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter.

Lastly, some simulations are given to validate the theoretical results.