Bifurcation and global stability in an eco-epidemic model with refuge

Maji, Chandan; Kesh, Dipak; Mukherjee, Dhiman

doi:10.1007/s40974-019-00117-6

Cited by 14 publications

(22 citation statements)

References 43 publications

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“…h. 7 ( (7) , (7) , 6 − 5 (1− 4 ) (7) , 3 (1− 3 ) (7) + 4 (1− 4 ) (7) − 3 ) is the interior equilibrium point, where (7) = (1+ (7) )(…”

Section: Equilibrium Point Of Mathematical Modelmentioning

confidence: 99%

“…Generally speaking, the ecoepidemiology model is divided into three cases. The first case is an only infected disease in prey as in [3]- [5]. The second case is an only infected disease in predator as in [6].…”

Section: Introductionmentioning

confidence: 99%

“…when the transmission disease increases significantly, then the number of infected population increases too [1]. In the model [3]- [8], the authors assume the simple mass incidence rate to represent the transmission disease in the model.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

Firdiansyah¹

2020

J. Mat. Mantik

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A predator-prey system with nonlinear incidence rate and refuging in prey is proposed to describe behavior change of certain infected diseases on healthy prey when the number of infected prey is getting large, while predator can predate prey by accessing refuging in prey. Therefore, this paper discusses the dynamics behavior predator-prey model with the spread of infected disease that is denoted by nonlinear incidence rate and adding prey refuge. We find the existence of eight non-negative equilibrium in the model, which their local stability has been determined. Furthermore, we also observe the prey refuge properties in the model. We find that prey refuge can prevent extinction in prey populations. In the end, some numerical solutions are carried out to illustrate our analytic results. For future work, we can investigate the harvesting effect in both populations, which is disease control in the predator-prey model with the spread of infected disease.

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“…h. 7 ( (7) , (7) , 6 − 5 (1− 4 ) (7) , 3 (1− 3 ) (7) + 4 (1− 4 ) (7) − 3 ) is the interior equilibrium point, where (7) = (1+ (7) )(…”

Section: Equilibrium Point Of Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

Firdiansyah¹

2020

J. Mat. Mantik

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“…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.…”

Section: Introductionmentioning

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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“…Present global scenarios show that human epidemiology has a significant impact on both the ecology and the environment. As this research article studies the modelling and control of an epidemic problem, the theoretical analysis of epidemiology is relevant to both ecology and environment (see Venturino et al 2016;Maji et al 2019;Khatua et al 2020, etc.). Moreover, the modelling approach using fractional-order differential equations gives an additional novelty and dimension of the article.…”

Section: Introductionmentioning

confidence: 99%

Modelling and control of a fractional-order epidemic model with fear effect

Mandal

Jana²,

Nandi³

et al. 2020

Energ. Ecol. Environ.

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In this paper, we formulate and study a new fractional-order SIS epidemic model with fear effect of an infectious disease and treatment control. The existence and uniqueness, nonnegativity and finiteness of the system solutions for the proposed model have been analysed. All equilibria of the model system are found, and their local and also global stability analyses are examined. Conditions for fractional backward and fractional Hopf bifurcation are also analysed. We study how the disease control parameter, level of fear and fractional order play a role in the stability of equilibria and Hopf bifurcation. Further, we have established our analytical results through several numerical simulations.

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Bifurcation and global stability in an eco-epidemic model with refuge

Cited by 14 publications

References 43 publications

Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

Dynamics of Infected Predator-Prey System with Nonlinear Incidence Rate and Prey in Refuge

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

Modelling and control of a fractional-order epidemic model with fear effect

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