Chaos and its Control in an Eco-Epidemiological Model

Abstract

The interplay between ecological and epidemiological processes often leads to complex nonlinear dynamics, including oscillations and chaos, which significantly influence the stability and persistence of interacting populations. In this study, we formulate and investigate a nonlinear eco-epidemiological model that incorporates a disease transmitted within the prey population under predator–prey interaction. The model is first nondimensionalized to reduce complexity and to highlight key dynamical parameters influencing system behavior. The equilibria and their stability are rigorously analyzed using the Jacobian matrix and Routh–Hurwitz criteria. Analytical conditions for the existence of biologically feasible steady states are derived, and the basic reproduction numbers R01 and R02 are computed to characterize disease invasion and persistence thresholds. Further, numerical simulations are conducted to demonstrate a rich variety of dynamical outcomes, including stable equilibria, limit cycles, and chaotic attractors. The onset of chaotic dynamics is confirmed through bifurcation analysis and Lyapunov exponent computation, revealing that predator interference and disease transmission parameters act as key bifurcation drivers. Moreover, a simple feedback control strategy is proposed and successfully applied to suppress chaotic oscillations and restore system stability. The findings highlight that even minimal parameter perturbations can induce irregular population fluctuations, whereas suitable control mechanisms can effectively regulate and stabilize the eco-epidemiological system. This study provides new insights into understanding and managing the emergence of chaos in disease-affected ecological systems