Dynamic Analysis of a VSEIR Model with Vaccination Efficacy and Immune Decline

Vaccination is an effective way to prevent the spread of infectious diseases. In this study, we formulate a VSEIR mathematical model to explore the effects of vaccination rate, vaccine efficacy, and immune decline on the COVID-19 transmission. The existence and stability criteria of equilibrium states were determined by analyzing the model. Model analysis was performed. One of the interesting phenomena involved in this issue is that diseases may or may not die out when the basic reproduction number falls below unity (i.e., a backward bifurcation may exist and cause multistability). The disease eventually becomes endemic in the population when the basic reproduction number exceeds one. By comparing different vaccination rates, vaccine efficacy, and infection rate factors, the diseases can be eliminated, not only by vaccines but also by strict protective measures. In addition, we used the COVID-19 number of reported cases in Xiamen in September 2021 to fit the model, and the model and the reported data were well matched.