Mathematical modelling of the dynamics of covid-19 pandemic

Abstract

A mathematical model to describe the dynamics of COVID-19 was formulated and analysed. The model is aimed at addressing the peculiarities of the dynamics of COVID-19 as identified by researchers as much as possible. Standard analysis indicates the existence of a disease-free equilibrium for the model which is locally-asymptotically stable when the basic reproduction number is less than unity. Conditions for the existence and stability of the endemic equilibria were determined. A backward bifurcation was found to be possible and triggered by the clinical progression of symptoms from asymptomatic to mild and to severe symptoms. Numerical simulation shows no significant difference in the dynamics of the asymptomatic and those with mild symptoms. The result also also shows that strict enforcement of quarantine can help contain the disease.