MATHEMATICAL MODELING OF ANTHRAX TRANSMISSION IN LIVESTOCK: THE CASE OF EAST HARARGIE ZONE, MELKA BELO WOREDA

Abstract

Anthrax is a disease caused by the bacterial Bacillus anthracis. It occurs in a worldwide and can infect a wide range of domestic and wild animal species. The deterministic mathematical model was developed and analyzed for the transmission dynamics of anthrax diseases in livestock by using six compartments: Susceptible(S), Vaccinated(V), Infected(I), Quarantine(Q), Recovered(R) and Contaminated environment(E). The study analyzed the qualitative behavior model such as: invariant region, positivity of the solution, existence and stabilities of the disease free equilibrium point and endemic equilibrium point. The basic reproduction number (

) was derived by using the next generation matrix method. The stability analysis result showed that disease free equilibrium point is locally and globally asymptotically stable when < 1 and unstable when > 1. The numerical simulation was conducted using Maple 18 software in order to investigate the effect of basic parameters in the expansion and the control of anthrax disease. The numerical simulation of model were performed to study the effects of vaccination, quarantine and burning of carcasses on infected livestock and the results displayed graphically showed that increasing rate of vaccination, quarantine and burning carcasses decreased the number of infected livestock with the anthrax disease. Therefore, It was concluded that the using combination of vaccination, quarantine and burning carcasses is used in controlling the transmission dynamics of anthrax disease.