An optimal control on the dynamics of wildebeest, zebra and lion prey predator interactions in Serengeti ecosystem

Abstract

In this paper we present an application of optimal control theory to assess the effectiveness of control measures of the dynamics of wildebeest, zebra and lion prey-predator system of Serengeti ecosystem. This is done by proposing control variables such as education (for retaliatory killing), construction of dams (for drought) and treatment (for infections). The main goal is to maximize the population density. For this aim, the Pontryagin’s maximum principle has been applied. The optimal control is characterized in terms of optimality system and solved numerically for several scenarios. Results shows that multiple optimal control measures is the most effective strategy in management of wildlife populations.