A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect

Abstract

We consider a system of delay differential equations to represent predator-prey eco-epidemic dynamics with weak Allee effect in the growth of predator population. The basic aim of the paper is to observe the dynamics of such system under the influence of gestation delay of predator and Allee parameter. We analyze essential mathematical features of the proposed model such as uniform persistence, stability and Hopf-bifurcation at the interior equilibrium point of the system. Global asymptotic stability analysis of the positive equilibrium points by constructing a suitable Lyapunov function for the delayed model is carried out separately. We perform several numerical simulations to illustrate the applicability of the proposed mathematical model and our analytical findings. We observe that the system exhibits chaotic oscillation due to increase of the delay parameter τ. We also observe that there is a threshold of Allee parameter above which the predator population will be washed away from the system.

Dynamical behavior of a generalized eco-epidemiological system with prey refuge

“…Eco-epidemiological systems, which are applied to describe predator and prey interactions with diseases in one population or both populations, have become important tools in analyzing the spread and control of infectious diseases, and hence have received much attention since the Kermac-Mckendric SIR model was proposed [1][2][3][4][5][6][7][8][9][10]. In eco-epidemiology, researchers study an ecological system with disease either in prey or in predator or in both populations [10][11][12][13][14][15][16]. Anderson and May [1] proposed an animal (predator) and plant (prey) model with infectious diseases and investigated the invasion, persistence, and spread of diseases.…”

“…Bairagi et al [10] noticed the fact that the functional response plays an important role in determining the dynamical consequences of the population interactions, and hence conducted a comparative research on the stability aspects of a predator-prey system with a class of functional responses. Besides the published works mentioned above, more and more researchers have focused on the population interactions with diseases in prey or predator or both populations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…However, most of published research on eco-epidemiological systems incorporated a certain response function (e.g., Holling type functional response, Beddington-DeAngelis functional response) and a certain incidence rate (e.g., bilinear incidence, standard incidence, and saturation incidence), and investigated the dynamical behaviors of the considered systems [10,11,[14][15][16]. As far as we know, few works have focused on a model with a generalized functional response and obtained a generalized conclusion.…”

Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator

“…One way to study these issues is through controlled laboratory experiments [20,22] , another useful way to study these types of problems is through mathematical modelling and computer simulations [59] . One of the such factors that can control chaos, is Allee effect [10,59] . There are two types of Allee effects: one is weak Allee effect, and the other one is strong Allee effect.…”

“…Recent studies on chaos and its control in ecological systems reveal the fact that Allee effect is an important factor through which the chaos can be enhanced [10,59] . However, the impact of Allee effect on a three-species system has been less studied.…”