Modeling and analysis of a predator–prey type eco-epidemic system with time delay

Haldar, Samadyuti; Khatua, Anupam; Das, Kunal; Kar, Tapan Kumar

doi:10.1007/s40808-020-00893-9

Cited by 10 publications

(4 citation statements)

References 42 publications

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“…The primary aim of their article was to illustrate how delays and impulsive stochastic interference influence the dynamics of the system. In their research, Haldar et al [6] focused on modeling and analyzing an eco-epidemic system of the predator-prey type, incorporating time delays. While numerous models [2-5, 7, 8] have explored diseases in prey populations, there is a noticeable gap in understanding models involving diseases in predator populations.…”

Section: Introductionmentioning

confidence: 99%

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Rajawat,

Dhar,

Sinha

2024

Preprint

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In this paper, the system including communicable infection from prey to predator , represented by the growing rate of the prey as a healing of a predator’s, has been utilized to develop and analyze a four-dimensional, non-linear eco-epidemic model. In the context of the analysis, the exploration of all potential equilibrium points, along with an examination of their local stability conditions, has been conducted both with and without considering time delays. Additionally, the confirmation of the model’s positivity and boundedness has been carried out. The positive and negative impact of the proposed model on the prey-predator population has been investigated aided by sensitivity analysis where the presence and validence of Bifurcation were elucidated by the numerical studies. The parameters were identified which explained the influence of disease and recovery delay over the model population. A right base for the perception of the behavioural effects of the prey-predator on eco-epidemiology has been prepared through the theoretical result. Based on the analytical result furthermore, numerical simulations were done so that the authenticity of the author’s numerical analytical approach using parameter values may be verified.

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Section: Introductionmentioning

confidence: 99%

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Rajawat,

Dhar,

Sinha

2024

Preprint

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“…Time delay has a tremendous impact on system dynamics. Several ecoepidemiological models involving delay in different factors have been proposed and studied (see [13][14][15][16][17][18][19][20][21]). Additionally, the dynamics of disease are significantly influenced by the force of infection.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate

Hussien¹,

Naji

2023

Journal of Applied Mathematics

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In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcation by using normal form theory and center manifold theorem are identified. Additionally, using numerical simulations and a hypothetical dataset, various dynamic characteristics are discovered, including stability switches, chaos, and Hopf bifurcation scenarios.

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“…For example, Tiwari et al [10] proposed and analyzed a mathematical model for a predator-prey system with multiple Allee effect acting on the growth rate of the prey population. Haldar et al [11] formulated a delay-induced ecoepidemic model using a reconstructed Leslie-Gower-type growth rate and then analyzed the dynamics of the system with infection in the prey population. A predator-prey model with the additive Allee effect and the fear effect in the prey was presented and investigated by Lai et al [12].…”

Section: Introductionmentioning

confidence: 99%

Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021

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In the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

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Modeling and analysis of a predator–prey type eco-epidemic system with time delay

Cited by 10 publications

References 42 publications

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

Eco-epidemic Dynamics with Infected Communicable Infection from Prey to Predator: Effect of Recovery Delay for Predator

The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate

Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

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