Mathematical Modelling and Control of COVID-19 Transmission in the Presence of Exposed Immigrants

Reuben Iortyer Gweryina (Department of Mathematics, Joseph Sarwuan Tarka University, P.M.B 2373, Makurdi, Nigeria)
Chinwendu Emilian Madubueze (Department of Mathematics, Joseph Sarwuan Tarka University, P.M.B 2373, Makurdi, Nigeria)
Martins Afam Nwaokolo (Department of Mathematics and Statistics, Federal University Wukari, Nigeria)

Communication in Biomathematical Sciences
Vol. 4 No. 2 (2021)

In this paper, a mathematical model for COVID-19 pandemic that spreads through horizontal transmission in the presence of exposed immigrants is studied. The model has equilibrium points, notably, COVID-19-free equilibrium and COVID-19-endemic equilibrium points. The model exhibits a basic reproduction number, R0 which determines the elimination and persistence of the disease. It was found that when R0 < 1, then the equilibrium becomes locally asymptotically stable and endemic equilibrium does not exists. However, when R0 > 1, the equilibrium is found to be stable globally. This implies that continuous mixing of exposed immigrants with the susceptible population will make the eradication of COVID-19 difficult and endemic in the community. The system is also proved qualitatively to experience transcritical bifurcation close to the COVID-19-free equilibrium at the point R0 = 1. Numerically, the model is used to investigate the impact of certain other relevant parameters on the spread of COVID-19 and how to curtail their effect.