Dynamics of a Mathematical Model of Coral Reef Ecosystems with Harvesting of the Crown-of-Thorns Starfish - Alya Saphira; Dian Savitri; Riska Wahyu Romadhonia (Jambura Journal of Biomathematics (JJBM), 2026)
This study develops a marine ecosystem model involving three species: coral as the prey, Crown-of-Thorns Starfish (CoTS) as the intermediate predator, and Giant Triton as the top predator. The model is formulated to investigate the ecological dynamics associated with CoTS outbreaks, which have become a critical environmental issue due to their significant impact on coral cover and their association with the decline of natural predators. A tritrophic predator–prey model incorporating CoTS harvesting as a population control strategy is developed based on Holling Type I and Type II functional responses. The model is analyzed through equilibrium analysis, local stability analysis, and bifurcation analysis. The results identify three biologically relevant equilibrium points: the extinction of the intermediate predator and top predator populations ($E_1$), the equilibrium between the prey and the intermediate predator in the absence of the top predator ($E_2$), and the coexistence equilibrium of all three species ($E_3$). Numerical simulations show that the stability of $E_3$ is regulated by the harvesting parameter ($H$). A supercritical Hopf bifurcation occurs at $H ≈ 0.007968$, leading to the emergence of stable periodic oscillations when the harvesting rate is below this critical threshold. Stable coexistence of the three species is maintained within an intermediate harvesting range of $0.007968 < H < 0.338462$. However, excessive harvesting beyond the upper critical threshold disrupts the trophic structure and causes the system to transition to the top-predator-free equilibrium ($E_2$) through the extinction of the Giant Triton population. These findings highlight the importance of appropriate harvesting intensity in maintaining ecosystem stability. Insufficient CoTS harvesting results in persistent oscillatory dynamics, whereas excessive harvesting destabilizes trophic interactions by reducing prey availability for the top predator. Therefore, maintaining CoTS harvesting within an appropriate range is essential for preserving stable species coexistence and supporting the long-term resilience of coral reef ecosystems.