Dynamics of COVID-19 Outbreak and Optimal Control Strategies: A Model-Based Analysis

Abstract

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus, which spreads so fast in the inhabitants. The virus is transmitted through direct contact with respiratory droplets of an infected individuals through coughing and sneezing or indirect contact through contaminated objects or surface. In this article, a non-linear mathematical model is proposed and analyzed to manifest the impact of transmission dynamics of the COVID-19 pandemic based on Indian condition by considering asymptomatic and symptomatic infections. It is assumed that the transmission rates due to asymptomatic and symptomatic individuals are different. The basic reproduction number of the model is computed and studied the stability of different equilibria of the model in detail. The sensitivity analysis is presented to identify the key parameters that influence the basic reproduction number, which can be regulated to control the transmission dynamics of the disease. Also, this model is extended to the optimal control model and is analyzed by using the Pontryagin's Maximum Principal and solved numerically. It has been observed that the optimal control model gives better result as compacted to the model without optimal control model as it reduces the number of infectives significantly in a desired interval of time.