Modeling the transmission dynamics of anthrax disease in cattle and humans

Anthrax is a zoonotic disease caused by bacillus anthraces. In this study a deterministic mathematical model for transmission dynamics of anthrax in humans and animals is presented and quantitatively analyzed. To understand the dynamics of anthrax, the basic reproduction number $R_0$ which measures average new infections is computed using next generation matrix operator and analyzed by normalized forward sensitivity index. Analysis shows that anthrax transmission rate to animals, animals' natural death rate, anthrax natural death rate and animal's birth rate are the most sensitive parameters to the disease transmission dynamics. When animal recruitment and anthrax transmission rates increase, the basic reproduction number $R_0$ also increase proportionally. However, when animal natural and anthrax induced death rates increase, basic reproduction number $R_0$ decreases. Numerical simulations using Runge-Kutta method show that animals drive the dynamics of anthrax. The study suggests control strategies such as vaccination, fumigation and decomposition of carcasses to eradicate the disease.