A mathematical model of COVID-19 with an underlying health condition using fraction order derivative

Studies have shown that some people with underlying conditions such as cancer, heart failure, diabetes and hypertension are more likely to get COVID-19 and have worse outcomes. In this paper, a fractional-order derivative is proposed to study the transmission dynamics of COVID-19 taking into consideration population having an underlying condition. The fractional derivative is defined in the Atangana Beleanu and Caputo (ABC) sense. For the proposed model, we find the basic reproductive number, the equilibrium points and determine the stability of these equilibrium points. The existence and the uniqueness of the solution are established along with Hyers Ulam Stability. The numerical scheme for the operator was carried out to obtain a numerical simulation to support the analytical results. COVID-19 cases from March to June 2020 of Ghana were used to validate the model. The numerical simulation revealed a decline in infections as the fractional operator was increased from 0.6 within the 120 days. Time-dependent optimal control was incorporated into the model. The numerical simulation of the optimal control revealed, vaccination reduces the number of individuals susceptible to the COVID-19, exposed to the COVID-19 and Covid-19 patients with and without an underlying health condition.