Dynamics of a delay-diffusion prey-predator model with disease in the prey

Mukhopadhyay, Banibrata; Bhattacharyya, R.

doi:10.1007/bf02936062

Cited by 31 publications

(12 citation statements)

References 26 publications

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“…Then F is uniformly persistent. Refer to the proof in the literature in [20], we obtain the following conclusions based on Lemma 3.1. implies that the boundary equilibrium point E 2 is also a saddle point. That is, all the boundary equilibria are saddle points under the condition of 1 C ÂK dC˛< R < 1 C b.ˇCd/ emd .…”

Section: Lemma 31 ([23])mentioning

confidence: 55%

“…Refer to the proof in the literature in , we obtain the following conclusions based on Lemma .Theorem If

1 + \frac{θK}{d + α} < R < 1 + \frac{b (β + d)}{emd}

, system is uniformly persistent. If

R < 1 + \frac{θK}{d + α}

, or

R > 1 + \frac{b (β + d)}{emd}

, system is impermanent. Proof On the aforementioned analysis, we obtain that E 1 is always a saddle point, the condition

R > 1 + \frac{θK}{d + α}

indicates that the boundary equilibrium point E 3 is also a saddle point and E 2 exists. But the condition

R < 1 + \frac{b (β + d)}{emd}

implies that the boundary equilibrium point E 2 is also a saddle point.…”

Section: Boundedness Boundary Equilibria and Persistencementioning

confidence: 72%

“…Among these, time delay is an important factor that can form oscillation. Many authors have considered the delay factor in their systems, such as literatures in [16][17][18][19][20][21]. As discussed in the previous paragraph, the predator would be weakened because of preying on the infected prey, but it needs a period of time to occur.…”

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confidence: 99%

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Impact on the predator population while lethal disease spreads in the prey

Chen

Wen

2016

Math Methods in App Sciences

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An eco-epidemiological model is proposed to interpret the impact of an infectious disease on ecosystem, where prey is infected by lethal bacteria and the consumption of infected prey contributes to the negative growth of predator population. Of course, the required time delay is incorporated into the model. The biodiversity conservation is concerned. Stability, persistence, and bifurcation are carried out. Finally, numerical simulations are performed to support the theoretical analysis.

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Section: Lemma 31 ([23])mentioning

confidence: 55%

“…Refer to the proof in the literature in , we obtain the following conclusions based on Lemma .Theorem If

1 + \frac{θK}{d + α} < R < 1 + \frac{b (β + d)}{emd}

, system is uniformly persistent. If

R < 1 + \frac{θK}{d + α}

, or

R > 1 + \frac{b (β + d)}{emd}

, system is impermanent. Proof On the aforementioned analysis, we obtain that E 1 is always a saddle point, the condition

R > 1 + \frac{θK}{d + α}

indicates that the boundary equilibrium point E 3 is also a saddle point and E 2 exists. But the condition

R < 1 + \frac{b (β + d)}{emd}

implies that the boundary equilibrium point E 2 is also a saddle point.…”

Section: Boundedness Boundary Equilibria and Persistencementioning

confidence: 72%

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Impact on the predator population while lethal disease spreads in the prey

Chen

Wen

2016

Math Methods in App Sciences

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“…Although the dispersal system is a relatively simple model for the raid of prey species by predators in a spatial domain, the solutions exhibit an extensive spectrum of ecologically pertinent behavior. Spatiotemporal dynamics includes chaos and target patterns [13][14][15]. The study of such spatiotemporal dynamics is an intensive area of research, and there are still many unanswered questions concerning these solution types [15][16][17].…”

Section: Diffusive Structure and Its Dynamic Forcesmentioning

confidence: 99%

Diffusion Dynamics and Impact of Noise on a Discrete-Time Ratio-Dependent Model: An Analytical and Numerical Approach

Das

Srinivas

Gazi

2019

MCA

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The paper deals with the dynamical behavior of a discrete-time ratio-dependent predator–prey system. The predator dependence is one of the main concerns of the system. The stability analysis of this 2-dimensional map was carried out analytically. Numerical simulation was carried out to verify the analytical results. We analyzed some specific features that could arise in discrete system. Basin of attraction was found for the endemic equilibrium state. We extended the numerical simulation for the maximal Lyapunov exponent. The presence of positive Lyapunov exponent indicated chaotic behavior of the map. The sensitive dependence on initial condition is one of the criteria for a discrete system. We showed that the system is sensitive on the initial conditions. We also carried out the analysis of diffusion and impact of noise.

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“…Ecological populations suffer from various infectious diseases, which have a significant role in regulating population sizes . Mathematical studies of such eco‐epidemiological models have explored several unknown aspects of ecological population interactions (e.g., ). The recent review illustrates the progress in the field in the last two decades.…”

Section: A Brief Literature Surveymentioning

confidence: 99%

An eco‐epidemic model for infectious keratoconjunctivitis caused by Mycoplasma conjunctivae in domestic and wild herbivores, with possible vaccination strategies

Abbona

Venturino

2016

Math Methods in App Sciences

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In this paper, we propose an eco‐epidemiological predator–prey model, modeling the spread of infectious keratoconjunctivitis among domestic and wild ungulates, during the summer season, when they intermigle in high mountain pastures. The disease can be treated in the domestic animals, but for the wild herbivores, it leads to blindness, with consequent death. The model shows that the disease can lead infected herbivores or their predators to extinction, even if it does not affect the latter. Boundedness of solutions and equilibria feasibility are obtained. Stability around the different equilibrium points is analyzed through eigenvalues and the Routh–Hurwitz criterion. Simulations are carried out to support the theoretical results. Sensitivity with respect of some parameters is investigated. The prey vaccination as control measure is introduced and simulated, although at present, the vaccine is not yet available, but just being developed. It would then possibly eradicate the infection in the domestic animals, which are considered a disease reservoir. Copyright © 2016 John Wiley & Sons, Ltd.

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Dynamics of a delay-diffusion prey-predator model with disease in the prey

Cited by 31 publications

References 26 publications

Impact on the predator population while lethal disease spreads in the prey

Impact on the predator population while lethal disease spreads in the prey

Diffusion Dynamics and Impact of Noise on a Discrete-Time Ratio-Dependent Model: An Analytical and Numerical Approach

An eco‐epidemic model for infectious keratoconjunctivitis caused by Mycoplasma conjunctivae in domestic and wild herbivores, with possible vaccination strategies

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