Control of Predator Disease Dynamics Under Prey Refuge and Harvesting: A Fuzzy Computational Modeling Approach

The control of infectious diseases plays a critical role in safeguarding the health of species and ecosystems. In this study, we investigate the combined effects of prey refuge and harvesting as mechanisms to limit the spread of disease within predator populations. A deterministic model is developed to examine the system dynamics through local stability analysis of equilibria, and the framework is further extended to an uncertain setting via a fuzzified model. The analysis shows that for small refuge values, the system reaches a stable state where infected predators move toward extinction, while prey and susceptible predators exhibit strong oscillations. As the refuge increases, the system undergoes a Hopf bifurcation, transitioning from periodic oscillations to a stable interior equilibrium. Beyond a critical threshold, oscillations disappear entirely. Harvesting of susceptible predators reveals that moderate harvesting induces oscillatory behavior in both prey and susceptible predator populations, whereas excessive harvesting can drive both predator classes to extinction. Harvesting of infected predators, by contrast, consistently drives their extinction regardless of harvesting intensity, with the other populations maintaining oscillatory patterns. These results indicate that an appropriate combination of prey refuge and harvesting can serve as an effective strategy for disease control in predator populations.