Dynamics of Diseased-Impacted Prey Populations: Defense and Allee Effect Mechanisms (2505.01952v1)

Abstract: This study introduces an innovative framework for merging ecological and epidemiological modeling via the formulation of a sophisticated predator-prey model that addresses the intricacies of disease dynamics, the Allee effect, and defensive mechanisms through prey aggregation. Employing rigorous stability and bifurcation analyses, we identify multiple feasible equilibria and establish critical thresholds that influence population survival and extinction. Our mathematical model reveals that the intensity of the Allee effect plays a crucial role in shaping population recovery and disease persistence, offering pivotal insights into finite time extinction mechanisms. We further illustrate, through extensive numerical simulations, that adjusting susceptible prey aggregation strategically can substantially reduce disease transmission, emphasizing the applicability of our findings for practical conservation interventions. The combined modulation of the aggregation constant and Allee effect determined three primary ecological outcomes: stable coexistence, elimination of infected prey, and complete population extinction. Moreover, these results have significant implications for wildlife management and ecosystem resilience, providing a solid theoretical framework for interdisciplinary strategies aimed at protecting endangered species.