Analysis of the dynamics of anthrax epidemic model with delay

Anthrax is a potentially fatal infectious zoonotic disease caused by the spore-forming bacterium Bacillus anthracis. While it is a disease of herbivores which primarily affects livestock and wildlife, it could also lead to serious and lethal infections in humans. Its large-scale outbreak could result in devastating economic impact related to losses in livestock and livestock products. Due to its ability to cause widespread disease and death, Anthrax has also become one of the numerous biological agents that is being considered in biowarfare and bioterrorism. Therefore, the modelling and analysis of Anthrax dynamics is crucial for the proper understanding of its prevention and control. In the present study, we investigate the nonlinear dynamics of Anthrax with delay effects which incorporates the mechanism of its incubation period. The sensitivity of the reproduction number dynamics with the model parameters is studied. The local and global stabilities of the model are studied. It is shown that the delay mechanism plays an important role in the dynamics of disease propagation. Mathematical considerations of a Susceptible-Infected (SI) delayed model to describe the propagation of Anthrax are proposed.We analytically derive the reproductive number and the equilibrium with and without anthrax. Necessary and sufficient conditions for the stability of the equilibria are mathematically established.The simulations confirm the analytical and numerical results derived in this work.