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

摘要

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 lt 1 $, while endemic equilibrium point $E_* $ is globally asymptotically stable for $R_0 gt 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.