Global stability of an anthrax model with environmental decontamination and time delay

Abstract

Anthrax occurs worldwide and is associated with sudden death of cattle and sheep. This paper considers an epidemic model of anthrax in animal population, only. The susceptible animal is assumed to be infected, only, through ingestion of the disease causing pathogens. The proposed model incorporates time delay and environmental decontamination by humans. The time delay represents the period an infected animal needs to succumb to anthrax-related death. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model fully hinges on whether the associated reproductive number is greater or less than unity. The effectiveness of environmental decontamination on eradication of anthrax in the community is explored through the reproductive number.