A Year Into the Pandemic: A Mathematical Model and Study of COVID-19 in India

Abstract

COVID-19 has been declared as a global pandemic by the World Health Organization (WHO) since its outbreak in December 2019. In India, as of May 12th 2021, the total number of coronavirus cases and associated deaths are 2,35,57,676 and 2,56,617 respectively. To control the spread of the virus effectively, social distancing, self-isolation and quarantine, lockdowns and mass inoculation are vital. In this paper we propose a deterministic epidemic model which is an extension of the SEIR model to understand the disease dynamics.The proposed model has eight compartments, Susceptible1, Susceptible2, Exposed, Infected, Quarantined, Isolated, Recovered and Dead and is termed as the S1S2EIQJRD model. The basic reproduction number Ris derived for the proposed model and it is shown that for the disease dies out and for the disease is endemic. Numerical simulations for the growth of the virus across India through the span of the outbreak are obtained. The simulation is done on real data and the results obtained may be used to make suitable inferences about the dynamics of the disease and appropriate measures can be taken to control its spread.