Abstract:
A new model for the transmission dynamics of Mycobacterium tuberculosis and bovine tuberculosis in a community, consisting
of humans and African buffalos, is presented. The buffalo-only component of the model exhibits the phenomenon of backward
bifurcation, which arises due to the reinfection of exposed and recovered buffalos, when the associated reproduction number is
less than unity.This model has a unique endemic equilibrium, which is globally asymptotically stable for a special case, when the
reproduction number exceeds unity. Uncertainty and sensitivity analyses, using data relevant to the dynamics of the two diseases in
the Kruger National Park, show that the distribution of the associated reproduction number is less than unity (hence, the diseases
would not persist in the community). Crucial parameters that influence the dynamics of the two diseases are also identified. Both
the buffalo-only and the buffalo-humanmodel exhibit the same qualitative dynamicswith respect to the local and global asymptotic
stability of their respective disease-free equilibrium, as well as with respect to the backward bifurcation phenomenon. Numerical
simulations of the buffalo-humanmodel showthat the cumulative number ofMycobacteriumtuberculosis cases inhumans (buffalos)
decreases with increasing number of bovine tuberculosis infections in humans (buffalo).
