SIR Model for COVID-19 Dynamics Incorporating Clinical Management

Abstract

In this paper, a mathematical model for COVID-19 disease incorporating clinical management based on a system of Ordinary Differential Equations is developed. The existence of the steady states of the model are determined and the effective reproduction number derived using the next generation matrix approach. Stability analysis of the model is carried out to determine the conditions that favour the spread of COVID-19 disease in a given population. The Disease Free Equilibrium is show to be locally asymptotically stable when \(R\)e < 1 and the Endemic Equilibrium is locally asymptotically stable when \(R\)e > 1. The Disease Free Equilibrium is shown not to be globally asymptotically stable using a technique by Castillo Chavez and the Endemic Equilibrium is shown to be globally asymptotically stable by means of Lyapunov's direct method and LaSalle's invariance principle. This implies that COVID-19 disease transmission can be kept low or manageable with the incorporation of clinical management. Sensitivity analysis of the model is carried out by use of the normalised forward sensitivity index (elasticity) which shows that the higher the rates of clinical management the lower the rate of infection. Numerical simulations carried out using MATLAB software showed that with high success of clinical management, there is low contact rate and low prevalence rate of the disease in the population.