DYNAMICS OF THE LESLIE-GOWER PREDATOR-PREY MODEL WITH THE BEDDINGTON-DEANGELIS RESPONSE FUNCTION, INCLUDING THE PRESENCE OF INFECTED PREY AND THE FEAR FACTOR OF SUSCEPTIBLE PREY TOWARD PREDATORS

Abstract

This article presents a stability analysis of the Leslie-Gower predator-prey model that is extended by taking into account prey infection, the presence of prey fear factors towards predators and the Beddington-DeAngelis response function. The Leslie-Gower model is a classic model that describes the dynamics of predator and prey populations, while the Beddington-DeAngelis response function accommodates the effects of population density and more complex interactions between predators and prey. The infected prey factor describes the prey's resistance to predator attacks becoming weak, while the prey fear factor towards predators affects prey growth. This study combines the components of infection in the prey population and the prey fear factor into the model to reflect the dynamics of disease and fear factors that can affect model stability. The model studied uses the Beddington-DeAngelis response function which describes the interaction between the prey population and the predator. This study uses two methods, namely analytical methods and numerical simulations. Analytical methods to study the stability analysis of the equilibrium point of the model by exploring the conditions under which the equilibrium point of the model is stable or unstable, focusing on the influence of infection parameters and the Beddington-DeAngelis response function on the stability of the equilibrium point. The results of the analysis show that prey infection and the shape of the response function can significantly affect the stability of the Leslie-Gower predator-prey model. The last section of this article presents numerical simulations that illustrate the stability of the equilibrium point of the model

Keywords

• leslie-gower
• beddington-deangelis function
• stability analysis
• numerical simulation.