Mathematics of FIV and BTB dynamics in buffalo and lion populations at Kruger National Park

Abstract

A new deterministic model for the transmission dynamics of feline immunodeficiency virus (FIV) and bovine tuberculosis (BTB) in lion‐buffalo population is designed and used to gain insight into the transmission dynamics of the two diseases in the population. The model is shown to undergo a backward bifurcation (a dynamic phenomenon characterized by the coexistence of the stable disease‐free equilibrium and a stable endemic equilibrium when the associated reproduction number of the model is less than unity). Two sources for this dynamic phenomenon, namely, the BTB reinfection of exposed buffalos and the BTB‐FIV co‐infection of lions, have been identified. It is shown that, for the special case of the model when backward bifurcation does not occur, the disease‐free equilibrium of the resulting model is globally‐asymptotically stable when the associated reproduction number is less than unity. Numerical simulations of the model, using initial and demographic data relevant to the BTB‐FIV dynamics in Kruger National Park, show that control strategies, such as the isolation of lions with FIV symptoms or the treatment of lions and buffalos with BTB symptoms, can lead to the effective control or elimination of the disease in the lion‐buffalo population if their effectiveness level is high enough. The time to elimination of any of the two diseases is significantly reduced if the strategies are combined.