Modeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Model

Abstract

A mathematical model is proposed and analysed to study the dynamics of two-prey one predator system of fishery model with Holling type II function response. The effect of harvesting was incorporated to both populations and thoroughly analysed. We study the ecological dynamics of the Nile perch, cichlid, and tilapia fishes as prey-predator system of lake Victoria fishery in Tanzania. In both cases, by nondimensionalization of the system, the equilibrium points are computed and conditions for local and global stability of the system are obtained. Condition for local stability was obtained by eigenvalue approach and Routh-Hurwitz Criterion. Moreover, the global stability of the coexistence equilibrium point is proved by defining appropriate Lyapunov function. Bioeconomic equilibrium is analysed and numerical simulations are also carried out to verify the analytical results. The numerical results indicate that the three species would coexist if cichlid and tilapia fishes will not be overharvested as these populations contribute to the growth rates of Nile perch population. The fishery control management should be exercised to avoid overharvesting of cichlid and tilapia fishes.

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

“…Once of the important results they obtained is that, all population would co-exist if any removal (death rate, harvesting and predation) were not below the intrinsic growth rate of every species. The same results were also obtained in [12] where was modelling the interaction of cichlid fishes, tilapia fish and Nile perch of lake Victoria ecosystem where they formulated the following model.…”

“…Here the author also assumed that every was harvested. Both [9] and [12] tried to model ecosystems by including more important factors. Other reviewed literature of the same scheme of modelling as the previous are [38] [39] [40].…”

“…There are various ways in which living things can interact, that is by commensalism, competition, predation and mutualism [10]. However, the interaction between predator and their own prey (prey-predator interactions) continues to be one of the dominant areas of research in mathematical ecology due to its universal existence, complexity and importance [11] [12]. For this reason, we believe that, this review may be of particular interest to those researchers involved in modelling this kind of biological and ecological problems allowing them to have an overview of the work which is currently being carried out.…”

Stability Analysis of Prey-Predator Model Migration with Holling Type-III Response Function in The Presence of Competition and Toxicity

“…The prey population that migrates back and forth in these two zones is assumed to increase logistically with the risk of natural death occurring due to several factors during migration. In this paper, the coefficient of interspecies competition between prey is also added according to the characteristics of the prey according to the authors [10], [27]. Prey are assumed to absorb heavy metal toxins from environmental pollution when migrating in reservation and unreservation zones following the author [22]- [24].…”

A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy

“…Such a kind of models divides the studied population (humans, animals, etc.) into different compartments representing individuals' states [14][15][16][17]. e spread of information is similar to the spread of diseases; consequently, the above models are widely considered.…”