Global stability analysis of a COVID-19 epidemic model with incubation delay

Abstract

In this paper, we propose, analyze and simulate a time delay differential equation to investigate the transmission and spread of Coronavirus disease (COVID-19). The basic reproduction number of the model is determined and qualitatively used to investigate the global stability of the model's steady states. We use numerical simulations to support the analytical results in the study. From the simulation results, we note that whenever the basic reproduction number is greater than unity, the model solutions will be associated with periodic oscillations for a considerable time scale from the start before attaining stability. This suggests that the inclusion of the time delay factor destabilizes the endemic equilibrium point leading to periodic solutions that arise due to Hopf bifurcations for a certain time frame.

Keywords

• global stability
• time delay
• epidemic model
• hopf bifurcation