Mathematical Analysis of the Effects of Controls on the Transmission Dynamics of Anthrax in Both Animal and Human Populations

Abstract

A nonlinear differential equation model is proposed to study the impact of vaccination on the transmission dynamics of anthrax in both livestock and human populations. The model is shown to exhibit only two equilibria, namely, the disease-free and the endemic equilibrium points, which are proven to be locally stable if the basic reproduction number (ℛ0) is less than unity and greater than unity, respectively. Local sensitivity analysis shows that the infection rate, pathogen-shedding rate, and rate of vaccination of livestock are parameters with the most positive impact on disease spread, whereas the rate of disinfection followed by the rate of vaccination are the parameters with the most negative impact on disease spread. Numerical simulation shows that implementing all control measures (i.e., vaccination, education, disinfection, and treatment) is a most effective strategy to curb disease spread.