Mathematical Modelling of the Population Dynamics of Two- Prey and One- Predator Systems at the Human-Livestock-Wildlife Interface

Abstract

Understanding the population dynamics at the human-livestock-wildlife interface is key to managing zoonotic and cross-species diseases as well as maintaining ecosystem biodiversity at this interface. This necessitates elucidation of the effects of within and between species interactions and human activities such as farming and animal harvesting among others. Keywords: Prey-Predator Systems; Predation; Population Dynamics; Ecological Modelling; Harvesting Threshold In this study, a mathematical model was developed and analyzed to study the dynamics of two- prey (Uganda-kobs (kobus kob thomasi) and the buffaloes (Syncerus caffer)) and one-predator (the lions (Panthera leo)) system at the human-livestock-wildlife interface. The model was analysed qualitatively for equilibrium points and their stability and, upon parametrization based on data in literature, numerical simulations were performed. Our findings re-echoed/re-emphasized that, for co-existence of the three species, the rate of human harvesting of kobus kob thomasi needed to be maintained below the species’ intrinsic growth rate. Existence of such a critical harvesting threshold was demonstrated and any harvesting rate exceeding that threshold would lead to ultimate extinction of both the kobus kob thomasi and the Panthera leo. Our findings further revealed that, for their long-term survival, the predator needs not to focus only on the easy-to-catch prey but use a balanced approach to ensure continued survival of both prey species. We conclude that, given the field data limitations, our findings are rather preliminary and more of a basis for future studies geared towards improving management of ecosystems involving interacting species. Most importantly, this study demonstrates that mathematical models can play a significant role in tackling complex system dynamics to generate useful information to guide policy decisions.