Modelling the COVID-19 epidemic using delayed-impulsive differential equations

Presently the large focus of the world community is on controlling the spread of COVID-19 infection. As of 30 March 2021, the COVID -19 infection has already accounted 121 million people and 2.9 million deaths worldwide. Many vaccines are now been approved for the prevention of COVID-19. Particularly in India as per government data available on 30 March 2021 more than 60 million people have been vaccinated. Forecasting is important for the alleviation of potentially fatal impacts of infectious diseases. In a pandemic, pronouncements are given in short supply of data in uncertain conditions. Also, this is not possible to know when the next pandemic will occur; however, mathematical modeling has the potential to increase the efficacy when a pandemic occurs. We analyze the Susceptible-Exposed-Infected-Vaccinated-Recovered (SEIVR) epidemic mathematical model of COVID-19. Our model includes two important aspects of COVID-19 infection: delayed start and effect of impulsive vaccination. The model has been analyzed theoretically and numerically both. We found that the COVID-19 infection-free periodic solution is globally asymptotically stable. Numerical simulations further show that impulsive vaccination with the vaccine of high efficacy will have the potential to reduce the spread of COVID-19 infection.