Mathematical Model for the Dynamics of Anthrax in Human and Animal Populations Incorporating Control Measures

Abstract

Anthrax is a zoonotic infectious disease caused by the bacterium Bacillus anthracis. In this study, we develop and analyze a deterministic compartmental model, formulated using ordinary differential equations, to explore the transmission dynamics of anthrax between humans and animals. Fundamental properties of the model, such as positivity, boundedness, and the existence of equilibrium points are established, confirming that the model is mathematically and biologically well-posed. The basic reproduction number, ​, is derived using the next-generation matrix approach. Stability analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable when . Additionally, the model possesses a unique endemic equilibrium when , which is also globally stable when . Numerical simulations are conducted to validate and illustrate the theoretical results.