2015
DOI: 10.1016/j.mbs.2015.02.013
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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 … Show more

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Cited by 35 publications
(21 citation statements)
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“…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.…”
Section: Introductionmentioning
confidence: 99%
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“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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].…”
Section: Introductionmentioning
confidence: 99%
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“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%