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, (Formula presented.), 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, (Formula presented.) while in their absence (Formula presented.). This supports its analytical solution that the disease-free equilibrium point (Formula presented.) is asymptotically stable whenever (Formula presented.), while endemic equilibrium point (Formula presented.) is globally asymptotically stable for (Formula presented.). 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.