Coronavirus disease: A mathematical approach to analyzing its transmission dynamics

Abstract

The novel Coronavirus Disease (also known as COVID-19) remains a persistent global health threat requiring continuous monitoring and protection of vulnerable populations. Current global surveillance highlights the persistence reoccurring of the disease in some parts of the world, hence the need for understanding its transmission dynamics. In this research, a mathematical model was developed to analyse the transmission dynamics of the disease amongst human population. The model shows the dynamical flow of the virus from person to person using a schematic diagram which was then translated into a system of ordinary differential equations comprising equations for susceptible individuals, exposed individuals, infectious individuals, individuals undergoing treatment and recovered individuals. The models validity and epidemiological significance was confirmed. Key metrics, including the epidemic indicator R0 are calculated using the next generation matrix approach and the equilibrium states were identified while the local and global stabilities of the disease free equilibrium were investigated using Jacobean matrix approach and Lyapunov function respectively. The global asymptotic stability of the endemic equilibrium was also investigated using Lyapunov function. With normalized forward sensitivity indices, sensitivity analysis was carried out to know the critical parameters influencing Covid-19 transmission. The discovery offers promising strategies in mitigating Covid-19 prevalence.