Global stability analysis and optimal prevention of COVID-19 spread in Ghana: A compartmental modelling perspective

Abstract

COVID-19 exposed most of the world healthcare systems as many countries were compelled to request for international support. The disease spreads through contact with bodily fluids of the infected person. COVID-19 poses great threat to people in old age with the disease’s severity risks factor borne by them. In this study, we developed a Covid-19 that explains the transmission mechanism of the disease. Model’s equilibrium points were determined and local stability analyses of the model at equilibrium was carried out. The analyses showed that disease free-equilibrium is stable when R₀<1 and unstable when R₀>1. Global stability analyses were also performed for the models using analytic methods of Lyapunov function approach. The model is then extended to optimal control by adding time-dependent controls. The model was analysed qualitatively with Pontryagin’s Maximum principle. Numerical simulations were carried out for the model by designing an iterative scheme that used a fourth-order Runge Kutta method. The numerical analyses also determine the effective strategy in controlling the disease. Best control strategy is education and sensitisation of the public on the dangers and possible causes of the infection.