Squids-snapper fish dynamics model with fishing effects in Terengganu, Malaysia

Abstract

Overexploitation of marine resources by human activities has become a pandemic issue nowadays. High fishing rates for example, may lead to the extinction of marine populations. In this paper, we introduce a mathematical model of prey-predator system for marine ecosystem with fishing rates for the case of Terengganu state. For this model, we use squids as prey while snapper fish as predator. The objectives of this paper are to analyze the sustainability of equilibrium populations of squids and snapper fish using stability analysis and to show the effect of fishing rates on both of these populations. This model shows that there are four potential equilibria solutions where both populations of squids and snapper fish may be extinct, mutual exclusions where either one of the species dies out as well as coexistence of both populations. The results for stability analysis reported that the equilibrium of coexistence of both populations was stable while the other was unstable. This means that populations of squids and snapper fish are estimated to sustain in the future with the current fishing activities in Terengganu. Hence, we conjectured that in order to guarantee both populations continue to exist, the fishing activities in Terengganu must be restricted within certain range of parameters that is lower than the population growth rates.