Effects of Over-Harvesting and Drought on a Predator-Prey System with Optimal Control

Abstract

In this paper, a two species predator-prey model is developed where prey is affected by over-harvesting and drought and predator is affected by drought. The intention is to investigate the impact of over-harvesting and drought on predator-prey system, and suggest control strategies to alleviate the problem of loss of prey and predator species due to over-harvesting and drought. The control strategies suggested are creation of reserve areas with restriction of harvesting for controlling over-harvesting and construction of dams for mitigating drought effects. The results obtained from theoretical and numerical simulation of the predator-prey model with harvesting and drought without control strategies showed that, both harvesting and drought affect the predator-prey population negatively. However, the results obtained from numerical simulations of the model with control measures showed that, the use of control strategies one at a time encourages the increase of the prey and predator species to the optimal population size. Furthermore, the best result is obtained when control strategies, creation of reserve areas with restriction of harvesting and construction of dams are applied simultaneously.

Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level

“…In recent years, the development of research on predator-prey mathematical models and harvesting by mathematicians has extended to marine reserves (can be seen in [17]). Mapunda et al [18] studied the predator-prey system by considering the creation of a marine reserve as a solution to over-exploitation and drought in the system. Based on their results, when the creation of marine reserves is not performed, it will have a negative impact on the predator and prey populations.…”

Michaelis-Menten Models with Constant Harvesting of Restricted Prey Populations Minimum Place and Amount Capacity

“…The cause of the extinction of the Prey is also influenced by over-harvesting. Therefore, it is necessary to limit the number of prey so that the number of prey remains under control and does not exceed the existing capacity [3] .…”