A Study on Corona Virus Transmission Dynamics: Stability and Hopf Bifurcation Analysis of the SIR Model with Time Delay

Abstract

In this research, we use the SIR (Susceptible, Infectious, and Recovered) model framework to mathematically simulate the spread of Corona virus Disease (COVID-19) in India. The effect of delay is accounted for by include a Hopf bifurcation parameter, and the research is limited to two states in India: Telangana and Andhra Pradesh. Local asymptotic stability of both the disease-free and epidemic equilibria is investigated. The ODE model indicates that the fundamental reproduction number R0 is tightly influenced by the dynamics. In circumstances where R0 is smaller than 1, the disease-free equilibrium is judged stable, leading to the extinction of the illness. When R0 is greater than 1, on the other hand, a special endemic equilibrium develops. The purpose of this article is to provide an initial value estimate for the COVID-19 pandemic in India using actual data. This particular SIR model for COVID-19 is one among several pandemic models currently under examination in India. Furthermore, the COVID-19 SIR model presented in this paper is applicable with or without time delay. Theoretical findings are substantiated through numerical experiments to enhance comprehension of the model's dynamics.