Fractional order Eco-Epidemiological model for the dynamics of a Prey-predator system

This study proposes a fractional-order eco-epidemiology model that incorporates the dynamics of three interacting species: a predator, prey, and infected prey. The model utilizes Holling Type I and Holling Type IV functional responses to describe predator-prey interactions and disease transmission within the prey population. By introducing fractional-order derivatives (where the order q is between 0 and 1), the model captures memory effects and non-local interactions, providing a more accurate representation of ecological and epidemiological systems compared to traditional integer-order models. The uniqueness and existence of solutions are established, and the local and global stability of equilibrium points are analyzed. Numerical simulations, using MATLAB, are conducted to demonstrate the system's behavior under various fractional orders and parameter values. The results show that fractional-order derivatives significantly influence the system's dynamics, leading to transitions from chaotic to stable behaviors as the value of q changes. Additionally, key system parameters, such as the hunting rate, half-saturation constant, and recovery rate of infected prey, are found to impact the stability and dynamics of the system. The study provides valuable insights into the role of fractional calculus in modeling complex predator-prey dynamics and disease spread, contributing to a better understanding of ecological stability, disease management, and species conservation.