Impulsive Control Strategies for Practical Exponential Stability and Disease Extinction in Stochastic Delayed Anthrax Models

ABSTRACT Stochastic environment and time delay have significant effects on the stability of anthrax. This study develops a time‐delayed stochastic anthrax model and explores sufficient conditions for the disease extinction. To effectively cope with disease outbreaks, we incorporate impulsive control strategies into the model and establish sufficient conditions for the system to attain mean square practical exponential stability. Through numerical simulations, it was observed that heightened noise and impulse intensity levels contribute to the disease's expedited extinction.