Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem

Abstract

In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control theory to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for controlling poaching, construction of dams for mitigating drought and vaccination for diseases control. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system plus a refuge factor is examined. All control strategies have shown significant increase in prey and predator populations. However, the best result is achieved by controlling all threats together. The effect of variation of prey refuge m to the control of threats is studied and results indicate that increase of m causes more prey individuals to be saved and reduces the number of predator individuals saved. This behaviour agrees with theoretical results obtained in coexistence equilibrium point.

Landscape Level Effects of Lion Presence (Panthera leo) on Two Contrasting Prey Species

“…Wildebeest are one of the most preferred prey species for lions (Hayward and Kerley, 2005), whereas impala are one of the least preferred (Owen-Smith, 2008). Both species are gregarious ungulates (Périquet et al, 2012;Sagamiko et al, 2015), impala are mixed feeders utilizing both grassland and bushland habitats according to seasonal change in food resources (Miranda et al, 2014), whilst wildebeest are regarded as grazers usually confined to grassland areas (Codron et al, 2007;Valeix et al, 2009;Périquet et al, 2012).…”

A Review of the Mathematical Models for the Impact of Seasonal Weather Variation and Infections on Prey Predator Interactions in Serengeti Ecosystem

“…Studying the influence of disease in the population dynamics of species in Serengeti ecosystem is potentially significant because they play a great role in stabilizing or distabilizing the ecosystem. For instance, it took more than ten years for Serengeti ecosystem to stabilize following the eruption of rinderpest disease in wildebeest as well as canine dispenser virus of 1994 in lion [6]. So far in many ecological studies of prey-predator systems with disease, it has been reported that predator take high parasites of infected prey [53] [54] [55] [56] [57].…”

“…Mathematical models can govern the time evolution of species in terms of their size, age, interactions, food supply, disease and environmental conditions including seasonal and climatic variations. Since all organisms in nature are interdependent [6], the interaction existing among them influences directly and indirectly the survival of each organism and the performance of the ecosystem in general. Hence, studying the comprehensive behaviour and dynamics of the ecosystem is vital for maintaining scientific management, ecological integrity of species and conservation of the ecosystem [7] [8] [9].…”

Modelling optimal control of harvested prey predator system incorporating a prey refuge

“…It is argued that harvesting prey predator species incorporating prey refuge should be done by good policy planning (Kar and Ghosh, 2012). Several studies have been conducted on optimal control strategies and management policies for sustainability of the ecological species such as reported by , Xiao and Ruan (2001), Cai et al (2008), Mayengo et al (2014), Sagamiko et al (2015). It is agreed that over-harvesting of prey -predator species has contributed to the loss of prey-predator populations.…”

“…They developed a two species of prey and predator model in which the predator was partially coupled with alternative prey aiming at studying the consequences of providing additional food to the predator as well as the effects of harvesting applied to both species, they observed that the provisional of alternative food to the predator was not always beneficial to the system however they used the effort pair as control parameters. Sagamiko et al (2015) proposed an optimal control of a threatened wildebeest-Lion preypredator in the Serengeti ecosystem. In their studies two threatened species prey-predator model were used in which the prey was Wildebeest and the predator was Lion.…”