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

Wang, Shufan; Ma, Zhihui; Wang, Wenting

doi:10.1186/s13662-018-1704-x

Cited by 20 publications

(10 citation statements)

References 33 publications

(53 reference statements)

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“…The three population exhibits an oscillatory behavior. Wang et al [38] points out that the increase of the infectious rate can lead to the lost of stability. Thus, our results are inline with the results of Wang et al [38] .…”

Section: Discussionmentioning

confidence: 99%

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

Melese

Feyissa

2021

Heliyon

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In this paper, we present and analyze a spatio-temporal eco-epidemiological model of a prey predator system where prey population is infected with a disease. The prey population is divided into two categories, susceptible and infected. The susceptible prey is assumed to grow logistically in the absence of disease and predation. The predator population follows the modified Leslie-Gower dynamics and predates both the susceptible and infected prey population with Beddington-DeAngelis and Holling type II functional responses, respectively. The boundedness of solutions, existence and stability conditions of the biologically feasible equilibrium points of the system both in the absence and presence of diffusion are discussed. It is found that the disease can be eradicated if the rate of transmission of the disease is less than the death rate of the infected prey. The system undergoes a transcritical and pitchfork bifurcation at the Disease Free Equilibrium Point when the prey infection rate crosses a certain threshold value. Hopf bifurcation analysis is also carried out in the absence of diffusion, which shows the existence of periodic solution of the system around the Disease Free Equilibrium Point and the Endemic Equilibrium Point when the ratio of the rate of intrinsic growth rate of predator to prey crosses a certain threshold value. The system remains locally asymptotically stable in the presence of diffusion around the disease free equilibrium point once it is locally asymptotically stable in the absence of diffusion. The Analytical results show that the effect of diffusion can be managed by appropriately choosing conditions on the parameters of the local interaction of the system. Numerical simulations are carried out to validate our analytical findings.

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Section: Discussionmentioning

confidence: 99%

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

Melese

Feyissa

2021

Heliyon

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“…A prey refuge may lead to population extinction or system's fluctuations. For example, a destabilization phenomenon appears because of prey refuge in an eco-epidemiological system [8]. Choosing different prey refuge decides whether undergoes Hopf bifurcation [9].…”

Section: Introductionmentioning

confidence: 99%

Analysis of an Eco-Epidemiological Model Considering Effect of Harvesting and Prey Refuge

Kang¹

2022

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In this work, we analyze an eco-epidemiological model with the disease in the prey, considering a constant proportion of harvesting of either species or a prey refuge. The positive invariant set, the conditions of existence, and locally asymptotically stability of the equilibria are studied using the stability theory of ordinary differential equation. The global stability of border equilibria by constructing Lyapunov functions and permanence of the system by comparison theoremare proved. The numerical simulation further proved the correctness of the theoretical analysis. The result indicates that overfishing would lead to population extinction and a reasonable fishing strategy should keep the coexistence of populations.

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“…The functionals f and g are respectively the interaction functionals for the first and second predator populations with the prey population. In the literature, there are a few papers that deal with a generalization of an interaction functional in a three-species model; we refer, for instance, to [29,37,45,[49][50][51], which give an additional motivation to our research. Furthermore, it is been also applied in understanding some epidemiological interactions; we refer, for example, to [3,4,16,17,31,36,[46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

Djilali

Ghanbari

2021

Adv Differ Equ

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The behavior of any complex dynamic system is a natural result of the interaction between the components of that system. Important examples of these systems are biological models that describe the characteristics of complex interactions between certain organisms in a biological environment. The study of these systems requires the use of precise and advanced computational methods in mathematics. In this paper, we discuss a prey–predator interaction model that includes two competitive predators and one prey with a generalized interaction functional. The primary presumption in the model construction is the competition between two predators on the only prey, which gives a strong implication of the real-world situation. We successfully establish the existence and stability of the equilibria. Further, we investigate the impact of the memory measured by fractional time derivative on the temporal behavior. We test the obtained mathematical results numerically by a proper numerical scheme built using the Caputo fractional-derivative operator and the trapezoidal product-integration rule.

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

Cited by 20 publications

References 33 publications

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

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

Analysis of an Eco-Epidemiological Model Considering Effect of Harvesting and Prey Refuge

Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

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