Dynamics of a Fractional Order Eco-Epidemiological Model

Abstract

This article discusses a fractional order eco-epidemiological model. The aim of considering the fractional order is to describe effect of time memory in the growth rate of the three populations. We investigate analytically the dynamical behavior of the model and then simulating using the Grünwald-Letnikov approximation to support our analytical results. It is found that the model has five equilibrium points, namely the origin, the survival of susceptible prey, the predator-free equilibrium, the free of infected prey equilibrium and the interior equilibrium. Numerical simulations show that the order of fractional derivative affects the behavior of solutions.

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

“…Hence, the dynamics of the relations between predators and their prey can be more accurately described by fractional-order systems [31,32]. Detailed background of the fractional-order differential equations can be found in [33][34][35][36][37][38][39][40][41]. Some previous studies indicate that the fractional-order system cannot have a periodic solution [42,43].…”

“…In [33,34] a kind of fractional order eco-epidemiological model with disease in the prey population was proposed and some issues related to theoretical and numerical analyses were investigated. However, the governing systems proposed in [33,34] are different from our fractional-order model (3). In this paper, we consider the following fractional-order eco-epidemiological model incorporating a predator's attack rate and half saturation constant:…”

Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey

“…Study of fractional-order differential equation becomes a popular research topic in science and engineering since various nonlinear phenomena can be described almost precisely by its ability [2], [5], [7], [10], [11], [14], [16], [31]. The main reason is that the fractional differential equation has capability to present the current state as a process that involves the history of the past states (or called the memory effects) [11], [8], [17], [23], [25], [27], [18]. Therefore, the fractional-order differential equation is gaining enormous enthusiasm from most researchers, especially in biological modeling such as ecological and epidemiological models or a combination of both which is called eco-epidemiological models [16], [18], [21], [22], [3], [20], [24], [26].…”

“…The main reason is that the fractional differential equation has capability to present the current state as a process that involves the history of the past states (or called the memory effects) [11], [8], [17], [23], [25], [27], [18]. Therefore, the fractional-order differential equation is gaining enormous enthusiasm from most researchers, especially in biological modeling such as ecological and epidemiological models or a combination of both which is called eco-epidemiological models [16], [18], [21], [22], [3], [20], [24], [26]. Here, we consider an eco-epidemiological model that studies the interaction between population of prey and its predator, where the prey population is assumed to grow logistically and may be infected by some microbiological organism such as pathogen or parasite.…”

Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator

“…Thus, fractional-order model gives interpretation of real phenomena realistically. Furthermore, the fractional-order model are naturally related to models with memory which exists in most biological models [11,12,13].…”