On the fractional-order modeling of COVID-19 dynamics in a population with limited resources

Abstract

Resource availability plays a pivotal role in the fight against emerging infections such as COVID-19. In the event where there are limited resources the control of an epidemic disease tends to be slow and the disease spread faster in the human population. In this paper, we are motivated to formulate and investigate a mathematical model via the Caputo derivative which incorporates the impact of limited resources on COVID-19 transmission dynamics in the population. We analyze the fractional model by computing the equilibrium points, and basic reproduction number, (R₀), and also used the Banach-fixed point theorem to prove the existence and uniqueness of the solution of the model. The impact of each parameter on the dynamical spread of COVID-19 was examined by the help of Sensitivity analysis. Results from mathematical analyses depict that the disease-free equilibrium is stable if R₀ < 1 and unstable otherwise. Numerical simulations were carried out at different fractional order derivatives to understand the impact of several model parameters on the dynamics of the infection which can be used to establish the influential parameter driving the epidemic transmission path. Our numerical results show that an increase in the recovery rate of hospitalization increases the number of infected individuals. The results of this work can help policymakers to devise strategies to reduce the COVID-19 infection.