Predator-prey populations with parasitic infection

Hadeler, K. P.; Freedman, H. I.

doi:10.1007/bf00276947

Cited by 394 publications

(235 citation statements)

References 24 publications

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“…Anderson and May [3] showed that invasion of a resident predator-prey or host-parasite system by a new strain of parasites could cause destabilization and exhibit limit cycles. Hadeler and Freedman [17] observed a similar phenomenon. Mukherjee [25] analysed a prey-predator model with parasite infection and obtained conditions for persistence and impermanence.…”

Section: Introductionmentioning

confidence: 60%

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

Mukhopadhyay

Bhattacharyya

2005

JAMC

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Abstract. A mathematical model dealing with a prey-predator system with disease in the prey is considered. The functional response of the predator is governed by a Hoilling type-II function. Mathematical analysis of the model regarding stability and persistence has been performed. The effect of delay and diffusion on the above system is studied. The role of diffusivity on stability and persistence criteria of the system has also been discussed.

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Section: Introductionmentioning

confidence: 60%

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

Mukhopadhyay

Bhattacharyya

2005

JAMC

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“…Anderson and May (1986) were considered the disease factor in a predator-prey dynamics and found that the pathogen tends to destabilize the predator-prey interaction. In Rosenzweig prey-predator model, an epidemic threshold (above which an infected equilibrium or an infected periodic solution appear) was determined by Hadeler and Freedman (1989). Chattopadhyay and Arino (1999) considered a three species eco-epidemiological model and determined extinction criteria of species and found condition for Hopf-bifurcation in an equivalent two-dimensional model.…”

Section: Introductionmentioning

confidence: 99%

Effects of additional food in a susceptible-exposed-infected prey–predator model

Sahoo

Poria

2016

Model. Earth Syst. Environ.

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In this paper, we propose a susceptible-exposedinfected prey-predator model supplying additional food to predator. We discuss the existence and the local stability conditions of both the disease free and endemic equilibrium points. Basic reproduction number is determined. The impact of additional food on infected prey population is discussed. Numerical simulation results establish that there exists a critical infection rate above which disease present in the system in absence of additional food. However, in such case supply of suitable additional food can make the system disease free. We compute the disease free regions in various parametric planes. Effects of variation of latent period is presented. Season dependent infection rate is also introduce in the system and the role of additional food is discussed. The main goal of this study is to show the nontrivial consequences of providing additional food for controlling infection in a diseased predator-prey system. This study is aimed to introduce a new non-chemical method for controlling disease of prey population.

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“…Modelling of trophic interactions in the presence of infection is a major subject of ecoepidemiology, which is itself a rapidly growing branch of theoretical ecology. Since the first publications in this area [3,13,34], hundreds of various ecoepidemiological models have been suggested so far emphasizing various aspects of the field (for a brief review, see [35]). However, in most of the previous works, the authors assume that the predator is a specialist, i.e.…”

Section: Introductionmentioning

confidence: 99%

A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

Sen

Banerjee

Морозов

2015

Math. Model. Nat. Phenom.

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Abstract. Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic ecoepidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.

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Predator-prey populations with parasitic infection

Cited by 394 publications

References 24 publications

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

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

Effects of additional food in a susceptible-exposed-infected prey–predator model

A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

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