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

Israr Ali, Hui Zhang (), Guobao Zhang, Ali Turab (), Li Wang and Jun-Jiat Tiang ()
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Israr Ali: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China
Hui Zhang: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China
Guobao Zhang: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Ali Turab: School of Software, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi’an 710072, China
Li Wang: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China
Jun-Jiat Tiang: Centre for Wireless Technology, CoE for Intelligent Network, Faculty of Artificial Intelligence & Engineering, Multimedia University, Persiaran Multimedia, Cyberjaya 63100, Selangor, Malaysia

Mathematics, 2025, vol. 13, issue 21, 1-21

Abstract: 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.

Keywords: predator–prey dynamics; disease control; prey refuge; harvesting strategies; fuzzy modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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