ABSTRACT
This paper presents a restricted SIR mathematical model to analyze the evolution of a contagious infectious disease outbreak (COVID-19) using available data. The new model focuses on two main concepts: first, it can present multiple waves of the disease, and second, it analyzes how far an infection can be eradicated with the help of vaccination. The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability. The basic reproduction number is calculated, and the positivity of the solutions is established. Numerical simulations are performed to determine if it is multipeak and evaluate vaccination's effects. In addition, the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.
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, R0 , 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, R0=0.698 while in their absence R0=3.8 . This supports its analytical solution that the disease-free equilibrium point E0 is asymptotically stable whenever R0<1 , while endemic equilibrium point E∗ is globally asymptotically stable for R0>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.