DYNAMICAL ANALYSIS OF A PREDATOR-PREY MODEL WITH A MULTIPLICATIVE ALLEE EFFECT ON THE PREY AND A STRUC-TURED PREDATOR POPULATION DIVIDED INTO SUSCEPTIBLE AND INFECTED CLASSES

Abstract

This study examines the interaction between prey and predator populations by incorporating a multiplicative Allee effect on the prey and disease infection in the predator. The mathematical model is constructed using a system of differential equations that integrates logistic prey growth, Holling type II functional response, and compartmental dynamics of healthy and infected predators. The analysis was carried out through nondimensionalization, linearization, and equilibrium point determination using the Jacobian matrix to investigate the local stability of the system. The results indicate that the system possesses several equilibrium points representing population extinction, prey-only existence, and coexistence of prey with either healthy or infected predators. The stability of these equilibria is strongly influenced by parameters such as the prey intrinsic growth rate, the Allee threshold, and the disease transmission rate. Numerical simulations demonstrate that the Allee effect can drive the prey population to extinction when its size falls below a critical threshold, while the disease in predators reduces the growth of healthy predators and thus contributes to the persistence of the prey population. This research enriches the field of mathematical ecology by providing new insights into the role of Allee effects and epidemiology in predator-prey dynamics.