A Michaelis–Menten Predator–Prey Model with Strong Allee Effect and Disease in Prey Incorporating Prey Refuge

Abstract

Here, we have proposed a predator–prey model with Michaelis–Menten functional response and divided the prey population in two subpopulations: susceptible and infected prey. Refuge has been incorporated in infected preys, i.e. not the whole but only a fraction of the infected is available to the predator for consumption. Moreover, multiplicative Allee effect has been introduced only in susceptible population to make our model more realistic to environment. Boundedness and positivity have been checked to ensure that the eco-epidemiological model is well-behaved. Stability has been analyzed for all the equilibrium points. Routh–Hurwitz criterion provides the conditions for local stability while on the other hand, Bendixson–Dulac theorem and Lyapunov LaSalle theorem guarantee the global stability of the equilibrium points. Also, the analytical results have been verified numerically by using MATLAB. We have obtained the conditions for the existence of limit cycle in the system through Hopf Bifurcation theorem making the refuge parameter as the bifurcating parameter. In addition, the existence of transcritical bifurcations and saddle-node bifurcation have also been observed by making different parameters as bifurcating parameters around the critical points.

Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge

“…The combined impact of Allee effect and prey refuge [15,16,20,22,28,32,34] on the predator-prey population dynamics enrich us to have better insight on species extinction. In the present decade, most of the researchers have considered Allee effect [18,24,37,38,46] on the prey species only.…”

Stability and bifurcation analysis of a diffusive modified Leslie-Gower prey-predator model with prey infection and Beddington DeAngelis functional response

“…Anderson and May [2] were the pioneers for investigating the invasion, persistence, and spread of infectious diseases by formulating an eco-epidemiological prey-predator model. At recent times, many researchers have proposed and studied epidemic and eco-epidemiological models [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] . For example, Shaikh et al [6] have investigated the dynamics of an eco-epidemiological system with disease in competitive prey species.…”

A stochastic eco-epidemiological system with patchy structure and transport-related infection

“…Some works studied the spread of diseases in predator/prey population in Lotka-Volterra type predation systems (Bhattacharyya and Mukhopadhyay 2010 ; Venturino 2002 ; Saha and Samanta 2019 ; Mainul 2010 ; Saha and Samanta 2020 ; Saha et al. 2018 ; Mondal and Samanta 2021 ). Hsieh and Hsiao ( 2008 ) and Fenton and Rands ( 2006 ) proposed a predator-prey system with disease in both prey and predator populations and considered the system dynamical behaviors.…”