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.
