Mathematical Model for Controlling the Spread of the Novel Covid-19 Virus: An Optimal Control Analysis. Case Study Ghana

Abstract

Worldwide governments faced the challenge of developing well-planned tailored strategies for controlling the COVID-19 pandemic to provide effective and efficient health protection while allowing economic and social activities to go on. This study uses the Susceptible- Exposed- Infected- Super spreaders- Hospitalized and Recovered (SEIPHR) which assumed that persons can equally likely to be infected with the virus in case of contact with an infected person except they are immune. The study performed numerical and qualitative analysis and different state variables were determined. The local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection were determined. The qualitative analysis results showed that the model has the disease-free equilibrium which was locally asymptotically stable for R0 < 1 and unstable for R0 ≥ 1. which clearly shows that, in the long run, close to 11% of the population was expected to be susceptible to the disease. The study also conducted sensitivity analysis. This analysis revealed that, the most important parameter is the contact rate. The optimal control analysis was carried out using the Pontryagins's maximum principle to determine the optimal strategy to curtail the spread of the disease. It was observed that, time optimal control existed in the model. The overall effect of the activation of all the control strategies simultaneously reduced the spread of the disease.