Stability Analysis of a relapse covid-19 mathematical model

Abstract

Coronavirus disease is a twenty-first century disease that forced the whole of human race into a compulsory recess during its pandemic. It is a global pandemic with several millions reported fatality cases. Efforts at curtailing the spread and reducing new infections eventually paid off when vaccines and therapeutic drugs were developed. However, battle against this disease is yet to be over, with statistics revealing that millions are still battling with the infection. One of the reasons for this is relapse, a condition of disease aggravation after it seems to subside. In this work, a mathematical model of covid-19 with relapse and immunity loss was developed and analyzed qualitatively. The equilibrium state of the model was found to exist distinctly as Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) respectively. Effective reproduction number of the model was computed, and numerical simulation showed a value that is greater than unity; an indicator that a break-out is certain whenever there is a contact with an infectious individual. Stability analysis of the model was computed and the system was numerically simulated. It was found that both recruitment and contact rates are major factors through which the disease can either be spread or curtailed.