Modeling elephant and poacher populations using the type IV functional response

Abstract

We develop and analyze a mathematical model for describing the population interactions between elephants and poachers. This model is a high-risk, high-reward predator-prey model in which the poachers are discouraged from hunting elephants by punitive laws, but motivated by the high profits gained from ivory. The poachers are assumed to exhibit a type IV functional response which allows for this high-risk, high-reward situation to be modeled. The research question aimed to be addressed with this model is to find an equilibrium point that results in the "coexistence" of elephants and poachers, and determine its long-term stability.