A mathematical model for COVID-19 transmission dynamics with a case study of India

Samui, Piu; Mondal, Jayanta; Khajanchi, Subhas

The ongoing COVID-19 has precipitated a major global crisis, with 968,117 total confirmed cases, 612,782 total recovered cases and 24,915 deaths in India as of July 15, 2020. In absence of any effective therapeutics or drugs and with an unknown epidemiological life cycle, predictive mathematical models can aid in understanding of both coronavirus disease control and management. In this study, we propose a compartmental mathematical model to predict and control the transmission dynamics of COVID-19 pandemic in India with epidemic data up to April 30, 2020. We compute the basic reproduction number R(0), which will be used further to study the model simulations and predictions. We perform local and global stability analysis for the infection free equilibrium point E(0) as well as an endemic equilibrium point E* with respect to the basic reproduction number R(0). Moreover, we showed the criteria of disease persistence for R(0) > 1. We conduct a sensitivity analysis in our coronavirus model to determine the relative importance of model parameters to disease transmission. We compute the sensitivity indices of the reproduction number R(0) (which quantifies initial disease transmission) to the estimated parameter values. For the estimated model parameters, we obtained [Formula: see text] which shows the substantial outbreak of COVID-19 in India. Our model simulation demonstrates that the disease transmission rate β(s) is more effective to mitigate the basic reproduction number R(0). Based on estimated data, our model predict that about 60 days the peak will be higher for COVID-19 in India and after that the curve will plateau but the coronavirus diseases will persist for a long time.