Study of LG-Holling type III predator–prey model with disease in predator

Shaikh, Absos Ali; Das, Harekrishna; Ali, Nida

doi:10.1007/s12190-017-1142-z

Cited by 28 publications

(20 citation statements)

References 41 publications

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“…In this paper, a delayed eco-epidemic model with LG Holling type III functional response is proposed by incorporating the negative feedback delay of the susceptible predator and the infected predator into the model formulated in the literature (Shaikh et al, 2018). Compared with the work by Shaikh et al (2018), we mainly focus on the effect of the time delay on the model and the model in the present paper is more general.…”

Section: Discussionmentioning

confidence: 99%

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Permanence and Hopf bifurcation of a delayed eco-epidemic model with Leslie–Gower Holling type III functional response

Zhang

Cao

Kundu

et al. 2019

Systems Science & Control Engineering

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This paper is concerned with a delayed eco-epidemic model with a Leslie-Gower Holling type III functional response. The main results are given in terms of permanence and Hopf bifurcation. First of all, sufficient conditions for permanence of the model are established. Directly afterward, sufficient conditions for local stability and existence of Hopf bifurcation are obtained by regarding the delay as bifurcation parameter. Finally, properties of the Hopf bifurcation are investigated with the aid of the normal form theory and centre manifold theorem. Numerical simulations are carried out to verify the obtained theoretical results.

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Section: Discussionmentioning

confidence: 99%

“…The proposed eco-epidemic model with LG Holling type III functional response in Shaikh et al (2018) is as follows…”

Section: Model Formulationmentioning

confidence: 99%

Permanence and Hopf bifurcation of a delayed eco-epidemic model with Leslie–Gower Holling type III functional response

Zhang

Cao

Kundu

et al. 2019

Systems Science & Control Engineering

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“…and 11 and 13 are as in Theorem 3.7.Hence, under condition(31) and the fact that 11 + 2 13 < 0 (cf. < 0 for all ≥ 0.…”

mentioning

confidence: 84%

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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“…We choose the same parameters of system (2) as those in [21]: = 3, = 5, 0 = 1.5, = 1, = 1, = 0.5, 1 = 1, 2 = 1, = 1, and = 0.5, while setting as the bifurcation parameter. Then, we get the specific case of system (2) as follows:…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Similarly, some scholars proposed and investigated the ecoepidemic models with disease in predators. Sarwardi et al [20] and Shaikh et al [21] studied a Leslie-Gower Holling type II predator-prey model with disease in predator and Leslie-Gower Holling type III predator-prey model with disease in predator, respectively. Some other ecoepidemic models with disease in predators one can refer to include [22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

Xia

Kundu

Maitra

2018

Journal of Function Spaces

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A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.

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Study of LG-Holling type III predator–prey model with disease in predator

Cited by 28 publications

References 41 publications

Permanence and Hopf bifurcation of a delayed eco-epidemic model with Leslie–Gower Holling type III functional response

Permanence and Hopf bifurcation of a delayed eco-epidemic model with Leslie–Gower Holling type III functional response

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

Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

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