Mathematical modeling of mutated COVID-19 transmission with quarantine, isolation and vaccination

Multiple variants of SARS-CoV-2 have emerged but the effectiveness of existing COVID-19 vaccines against variants has been reduced, which bring new challenges to the control and mitigation of the COVID-19 pandemic. In this paper, a mathematical model for mutated COVID-19 with quarantine, isolation and vaccination is developed for studying current pandemic transmission. The basic reproduction number $ \mathscr{R}_{0} $ is obtained. It is proved that the disease free equilibrium is globally asymptotically stable if $ \mathscr{R}_{0} < 1 $ and unstable if $ \mathscr{R}_{0} > 1 $. And numerical simulations are carried out to illustrate our main results. The COVID-19 pandemic mainly caused by Delta variant in South Korea is analyzed by using this model and the unknown parameters are estimated by fitting to real data. The epidemic situation is predicted, and the prediction result is basically consistent with the actual data. Finally, we investigate several critical model parameters to access the impact of quarantine and vaccination on the control of COVID-19, including quarantine rate, quarantine effectiveness, vaccination rate, vaccine efficacy and rate of immunity loss.