Persistence and extinction criteria of Covid-19 pandemic: India as a case study

Abstract

Novel coronavirus has altered the socio-economic condition of the whole world through its devastating effects on the human population. Mathematical models and computation techniques may play an important role in understanding this epidemic and contribute a lot in policy making to control the infection in a more systematic and effective way. In this paper, we have proposed a deterministic mathematical model for the Covid-19 pandemic taking into account the different epidemiological status of individuals of a given geographical region and analyzed it with respect to the basic reproduction number. Uncertainty is obvious in the case of a growing epidemic and it multiplies if the disease etiology is unknown. Taking into account the uncertainty in the epidemiological parameters, we extended the deterministic system into a stochastic system through random parameter perturbations in three epidemiological parameters. Analyzing the model, we determined the disease persistence and eradication conditions. The asymptotic behavior of the stochastic solution around the coexistence equilibrium of the deterministic model was also presented. As a case study, we considered the Covid-19 pandemic of India and estimated the model parameters from the epidemic data. We demonstrated different analytical results and predicted the course of the epidemic. Our simulation results indicate that the epidemic in India may continue up to third week of July 2021 and the cumulative confirmed Covid-19 cases may vary from $12.13\times {10}^6$ to $13.41\times {10}^6.$ Such results may be useful from management and policy development viewpoints.

Keywords:

• Covid-19 epidemic model
• white noise
• basic reproduction number
• asymptotic behavior
• parameter estimation
• Indian case study

Acknowledgments

We sincerely acknowledge the constructive suggestions of the anonymous reviewer in improving the manuscript.

Additional information

Funding

This work was supported by Council of Scientific and Industrial Research, India; Science and Engineering Research Board.