INNOVATIVE MATHEMATICAL MODELLING IN PREDATOR-PREY DYNAMICS: A SYSTEMATIC REVIEW
DOI:
https://doi.org/10.46754/jmsi.2024.10.006Keywords:
Predator-prey dynamics, Mathematical modelling, Ecology, Disease dynamics, Stability analysisAbstract
Advancements in mathematical ecology have greatly expanded predator-prey models beyond the classical Lotka-Volterra framework, incorporating complex factors such as role reversal, fractional calculus, and the Allee effect. This review highlights innovative models and advanced mathematical techniques that enhance our understanding of predator-prey dynamics and their applications across disciplines. It analysed recent studies introducing new ecological factors, including maturation delays, disease dynamics, and spatial heterogeneity. Techniques like fractional calculus and network theory were examined for their effectiveness in capturing complex behaviours. Models addressing role reversal between adult prey and juvenile predators or incorporating generalized fractional derivatives reveal significant impacts on population stability. Additionally, maturation delays, handling time, and gestation periods markedly influence oscillatory dynamics. The reviewed models demonstrate versatility in guiding pest control, understanding disease spread, and optimizing biotechnological processes. This review shows that modern predator-prey models, enriched by complex ecological factors and advanced mathematics, provide profound insights into system dynamics, with practical applications across various fields. As global challenges grow, these models offer crucial guidance for developing more resilient and sustainable systems, underscoring their potential to address
issues like food security, disease outbreaks, and ecosystem degradation. Future research should integrate emerging factors, such as anthropogenic noise and industrial pollutants, to further enhance the models’ real-world relevance.
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