A Mathematical Model of Black Rhino Translocation Strategy

Aldila, Dipo; Hutchinson, A.J.; Woolway, Matthew; Owen‐Smith, Norman; Soewono, Edy

doi:10.5614/j.math.fund.sci.2015.47.1.8

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…In order to increase the population of the rhino, a translocation strategy has been implemented [4]. A study about the impact of human intervention on different translocation strategies is discussed in [4,5]. Other efforts can also be applied to preserve white rhinos.…”

Section: Introductionmentioning

confidence: 99%

“…Their result suggests that dehorning should be done annually under some circumstances. The authors of [5] propose a mathematical model to describe a strategy to harvest rhinos such that the population can still survive. According to the above explanation and to the best of our knowledge, there are few mathematical models concerning the dynamics of southern white rhinos, especially since it was affected by illegal and legal poaching.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control problem arises from illegal poaching of southern white rhino mathematical model

2020

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In this paper, a novel dynamical population model of a southern white rhino with legal and illegal poaching activity is introduced. The model constructed is based on a predator–prey model with southern white rhinos as prey and humans (hunters) as predators. We divide the southern white rhino population into three classes based on their horn condition. We investigate the existence and the stability of the equilibrium points, which depend on some threshold functions. From an analytical result, it is trivial that arresting as many hunters as possible helps conserve white rhinos, but it comes at a high cost. Therefore, an optimal strategy is needed. The optimal control is then constructed using Pontryagin’s minimum principle and solved numerically with an iterative forward–backward method. Optimal control simulations are given to provide additional insight into the dynamics of the model. Analysis of the cost function effectiveness is conducted using the ACER (Average Cost–Effectiveness Ratio) and ICER (Incremental Cost–Effectiveness Ratio) indicator method. The results show that the hunter population can be more easily controlled with a time-dependent hunter arrest rate rather than by treating it as a constant.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control problem arises from illegal poaching of southern white rhino mathematical model

2020

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“…Based on the Lotka -Volterra model, when both species exist, a decrease in the number of prey populations and an increase in the name of predatory populations occur at a rate proportional to the frequency of encounters between individuals in both species [3]. Until today, many mathematical models have constructed by many authors based on the Lotka -Volterra model, such as [4], [5], [6]. In the other hand, there are several models which also combine the predatory models with diseases among prey or predator populations, such as in [7], [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%