Analysis and Optimal Control of an SEIHRVI Epidemic Model Based on Vaccination
In order to study the effect of vaccination on the control of infectious diseases,an epidemic model with standard incidence rate was developed.The basic reproduction number of the model was derived and the condition for the existence of the endemic equilibrium was given.By constructing Lyapunov function,the global stability of equilibrium was proved.Pontryagin's maximum principle was applied to analyze the optimal control problem and the optimal control strategy was obtained.The results showed that improving the vaccination rate and vaccine efficacy could effectively control the spread of the disease.Paying attention to self-protection,timely vaccination,and treatment could reduce the scale of disease outbreaks to a certain extent.