MODEL MATHEMATICAL ANALYSIS OF ANTHRAX TRANSMISSION ON HERBIVORES

Abstract

Anthrax is an infectious disease caused by the bacterium Bacillus Anthracis. Herbivores are susceptible to anthrax. The model of anthrax transmission taking into account the effect of vaccines on herbivores has two equilibrium points, namely disease-free equilibrium points and endemic equilibrium points. The Next Generation Matrix method is used to determine basic reproductive numbers 0 . The disease-free equilibrium point is achieved as a locally asymptotically stable state when 0  1 it means that anthrax is eradicated, while the endemic equilibrium point is reached asymptotically stable when 0  1 it means that anthrax existence exists. Numerical simulations show that the endemic or anthrax disease spread in populations of herbivorous animals. Keywords: Herbivores, Anthrax, Basic Reproduction Numbers, Vaccine, Local Stability.