Abstract:
This paper presents a two stage SIS epidemic model in animal population
with bovine tuberculosis (BTB) in African buffalo as a guiding example. The
proposed model is rigorously analyzed. The analysis reveals that the model
exhibits the phenomenon of backward bifurcation, where a stable disease-free
equilibrium (DFE) coexists with a stable endemic equilibrium (EE) when the
associated reproduction number (Rv) is less than unity. It is shown under
two special cases of the presented model, that this phenomenon of backward
bifurcation does not arise depending on vaccination coverage and efficacy
of vaccine. Numerical simulations of the model show that, the use of an
imperfect vaccine can lead to effective control of the disease if the vaccination
coverage and the efficacy of vaccine are high enough.
