A mathematical model of coral reef response on predator-prey interactions with delay

Abstract

Excessive and destructive fishing practices are some of the various anthropogenic stressors which are resulting in the destruction of the coral reefs. These practices not only degrade the reefs directly but also diminish the reef fishes that are mainly responsible for keeping the coral predators and it's competitors under control. The destructive effects are more prolific when cyanide or explosives are used on these reefs. In our present study, we investigate highly problematic corallivore Crown-of-thorns starfish (CoTS), \textit{Acanthaster planci}, and also its predator, Humphead wrasse, \textit{Cheilinus undulatus} which is overfished as well as endangered. A three-dimensional mathematical model is analyzed for the interaction of coral, wrasse and CoTS biomass in an open marine system. We study the commensalism among wrasse and coral in support of wrasse. Also, we take into consideration predator-prey relationships between wrasse and CoTS, and CoTS and coral. We further investigate and compare the dynamical behaviour of the non delay and delay systems. We also observe that by decreasing and increasing the values of conversion efficiency of corallivore predator and starfish respectively, the systems exhibit oscillatory dynamics. Computer simulations have been done to illustrate distinct analytical results.