Novel corona virus disease dynamical models with pulse vaccination

Abstract

Due to the widespread and serious prevalence of the 2019 novel corona virus disease (COVID-19), COVID-19, has seriously affected people’s lives and the economic development. To study the transmission dynamics of COVID-19 and find effective measures to control, prevent and ultimately eliminate COVID-19 are one of the main problems now. In this paper, we build a pulse mathematical model of COVID-19 with vaccination. Using the principle of stroboscopic mapping and the basic reproduction number R0, we show that if R0<1, the disease-free periodic solution is globally asymptotically stable; If R0>1, the model is persistent and there exists a positive periodic solution; Using the bifurcation theory, there is a supercritical bifurcation for the model if R0=1. Finally, the numerical simulation and sensitivity analysis shows that reducing the novel corona virus infection rate and increasing the cure rate are more effective than increasing the vaccination rate. In order to comprehensively and quickly control the spread of the epidemic, excepting for vaccination, some other measures need to be implemented, such as reducing the population exposure rate and using specific drugs, which provides useful suggestions for the governments to prevent, control and ultimately eliminate COVID-19.