Mathematical modelling on COVID-19 transmission impacts with preventive measures: a case study of Tanzania

Abstract

The outbreak of COVID-19 was first experienced in Wuhan City, China, during December 2019 before it rapidly spread over globally. This paper has proposed a mathematical model for studying its transmission dynamics in the presence of face mask wearing and hospitalization services of human population in Tanzania. Disease-free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. The trace-determinant approach was used in the local stability of disease-free equilibrium point while Lyapunov function technique was used to determine the global stability of both disease-free and endemic equilibrium points. Basic reproduction number, $R_0$ , was determined in which its numerical results revealed that, in the presence of face masks wearing and medication services or hospitalization as preventive measure for its transmission, $R_0=0.698$ while in their absence $R_0=3.8$ . This supports its analytical solution that the disease-free equilibrium point $E_0$ is asymptotically stable whenever $R_0<1$ , while endemic equilibrium point $E_{\ast }$ is globally asymptotically stable for $R_0>1$ . Therefore, this paper proves the necessity of face masks wearing and hospitalization services to COVID-19 patients to contain the disease spread to the population.

Keywords: COVID-19; basic reproduction number; equilibrium points and stability.