Modelling the Transmission Dynamics of Anthrax Disease with Simultaneous Vaccination for both Human and Animal Population Using the Saturated Incidence Rate

Abstract

In this study, a mathematical model based on saturated incidence rate that explores the transmission dynamics of anthrax as a zoonotic disease with vaccination compartment introduced into the human and animal population was formulated using ordinary differential equations. The model’s flow diagram was presented with qualitative and quantitative analysis carried out on the model. The local and global stability analysis of the equilibrium points investigated using the Ruth-Hurwitz criterion and Castillo-Chaves method respectively were found to be locally asymptotically stable if the basic reproductive number is less than one and unstable if the basic reproductive number is greater than one. Test for backward bifurcation was done with the result showing no backward bifurcation in the system. The sensitivity analysis of the model's parameters was performed to determine the contribution of each parameter to the basic reproduction number and a plot of partial ranking correlation (PRCC) obtained. The analysis revealed that, by decreasing human and animal contact rate, it would cause a decrease in the basic reproduction number. Also, numerical simulation further showed that increase in vaccination for both human and animal population reduces the spread of anthrax disease in the population. Anthrax disease, Bifurcation, Mathematical modeling, Sensitivity index, Stability