A Mathematical Model Analysis on Anthrax Disease Considering Environmental Spore Concentration

This study presents a mathematical model of an anthrax disease, which focuses on the role of the concentration of spores in the environment. The main objective is to analyse the dynamics of the disease and to assess the stability of its equilibrium points—in particular, those of the endemic and anthrax-free states. The relevance of this research is its potential to inform public health strategies for the management of anthrax attacks. This study used the Castillo–Chavez and LaSalle invariant principles to establish the boundedness, positivity, and existence of the solutions to the system. In addition, the basic reproduction number was calculated (R0) using the next-generation matrix approach and performed sensitivity analyses to assess the effect of parameters such as host-to-host transmission coefficient (β1), environmental transmission coefficient (β2), and spore production rate (p) on the R0 parameter. To confirm my analytical findings, numerical simulations have been performed to confirm that a decrease in these parameters leads to a decrease in reproductive rate. The simulation shows that if R0 < 1 is stable both locally and globally, the anthrax disease-free equilibrium is stable, indicating the presence of effective control measures. On the other hand, the endemic equilibrium is stabilised at R0 > 1, which highlights the need for immediate intervention.