Transmission Dynamics of COVID-19 Pandemic Non-pharmaceutical Interventions and Vaccination

Non-pharmaceutical interventions(NPIs) play an important role in the early stage control of COVID-19 pandemic. Vaccination is considered to be the inevitable course to stop the spread of SARS-CoV-2. Based on the mechanism, a SVEIR COVID-19 model with vaccination and NPIs is proposed. By means of the basic reproduction number $R_{0}$, it is shown that the disease-free equilibrium is globally attractive if $\mathscr{R}_{0}<1$, and COVID-19 is uniform persistence if $\mathscr{R}_{0}>1$. Taking Indian dates for example in the numerical simulation, we find that our dynamical results fits well with the statistical dates. Consequently, we forecast the spreading trend of COVID-19 pandemic in India. Furthermore, our results imply that improving the intensity of NPIs will greatly reduce the number of confirmed cases. Especially, NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is relatively low. By simulating the relation ships of the basic reproduction number $\mathscr{R}_{0}$, the vaccination rate and the efficiency of vaccine, we find that it is impossible to achieve the herd immunity without NPIs when the efficiency of vaccine is lower than $76.9\%$. Therefore, the herd immunity area is defined by the evolution of relationships between the vaccination rate and the efficiency of vaccine. In the study of two patchy, we give the conditions for India and China to be open to navigation. Furthermore, an appropriate dispersal of population between India and China is obtained. A discussion completes the paper.