Global Stability and Optimal Control for a COVID-19 Model with Vaccination and Isolation Delays

COVID-19 pandemic remains serious around the world and causes huge deaths and economic losses. To investigate the effect of vaccination and isolation delays on the transmission of COVID-19, we propose a mathematical model of COVID-19 transmission with vaccination and isolation delays. The basic reproduction number is computed, and the global dynamics of the model are proved. When R₀<1, the disease-free equilibrium is globally asymptotically stable. The unique endemic equilibrium is globally asymptotically stable if R₀>1. Based on the public information, parameter values are estimated, and sensitivity analysis is carried out by the partial rank correlation coefficients (PRCCs) and the extended version of the Fourier amplitude sensitivity test (eFAST). Our results suggest that the isolation rates of asymptomatic and symptomatic infectious individuals have a significant impact on the transmission of COVID-19. When the COVID-19 is epidemic, the optimal control strategies of our model with vaccination and isolation delays are analyzed. Under the limited resource with constant and time-varying isolation rates, we find that the optimal isolation rates may minimize the cumulative number of infected individuals and the cost of disease control, and effectively contain the transmission of COVID-19. Our study may help public health to prevent and control the COVID-19 spread.