Deterministic Mathematical Model and Analysis of Transmission Dynamics of Covid-19 from Reservoir-to-Human

This article presents a deterministic mathematical model for the transmission dynamics of covid-19 from the reservoir to the people was formulated. The model system properties was analysed such as feasibility of the solutions, positivity of the state variables,stability of the model equilibria both local and global equilibria points. Also, the basic reproduction number R0 was computed along its sensitivity for model parameters to identify the most persuading parameter and the results proved that high values of the parameters associated with the rate of controlling the infection out of human life back to reservoir will drasticallyminimized the spread rate of Covid-19 in people. The local stability of disease-free equilibrium was determined through the trace and determinant of matrix method. The disease-free equilibrium will be asymptotically stable if the tr(J+) < 0 and det(J+) > 0. The disease-freeand endemic equilibria was found to be globally stable when the R0 < 1 and R0 > 1 respectively. The analysis of the numerial simulation the model on various sets of parameters displayed that there is a strong noteworthy effect on the virulent if the efort of controlling the infection is at the rate of not less than 50% to pull back the infection out of people to reservoir or vanishing.