Modeling transmission dynamics and control of anthrax

Abstract

Anthrax is a zoonotic disease caused by Bacillus anthraces. In this study the deterministic mathematical models for transmission dynamics of anthrax in absence and presence of control strategies in humans and animals are presented and analyzed to determine which parameters are sensitive to the disease and how will control strategies help to eradicate the disease. Using normalized sensitivity index, sensitivity index of each parameter with respect to basic repro- duction number R0 is derived and find that, parameters such as anthrax transmission’s rate β , animal’s recruitment rate ba, animal’s natural death rate, and pathogen’s natural death rate are most sensitive to the transmission dynamics of anthrax. Stability analysis for equilibrium states by linearization, Metzler matrix, and Lyapunov function shows that the disease-free equilibrium is locally and globally asymptotically stable when R0 < 1 and endemic equilibrium is globally asymptotically stable when R0 > 1. The analysis shows that when free pathogens are destroyed with fumigants both susceptible humans and animals flourish while infected humans and an- imals decrease. It is also found that pathogens and carcasses decrease due to the fumigation effect. The analysis also shows that when carcasses are incinerated and removed from the af- fected area both humans and animals increase while infected humans and animals decrease. The analysis also shows that incineration and complete removal of carcasses makes the population of carcasses and pathogens decrease. The study also found that when all control strategies such as fumigation, incineration and complete removal of carcasses, animal’s treatment, and humans treatment are all administered both susceptible humans and animals increase, infected humans and animals decrease and carcasses and pathogens decrease.