Ecoepidemic models with prey group defense and feeding saturation

Gimmelli, Giacomo; Kooi, Bob W.; Venturino, Ezio

doi:10.1016/j.ecocom.2015.02.004

Cited by 52 publications

(60 citation statements)

References 30 publications

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“…However, here the prey-dependent hyperbolic relationship is expressed as a function of the "square root" of the prey size instead of the prey size itself. It differs from the herd behavior model presented in [1] , because it takes into account the feeding satiation phenomenon also explored in [8] . In the recent paper [4] a similar problem was studied but the predator groupdefending prey functional response was the Holling type IV instead of the "square root" functional response.…”

Section: Introductionmentioning

confidence: 99%

“…At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al, 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon.…”

Section: Introductionmentioning

confidence: 99%

“…In a parallel paper [8] an ecoepidemiological model in which the epidemics spread among the predators was proposed. Here we investigate a model where the prey are affected by a disease that propagates by contact.…”

Section: Introductionmentioning

confidence: 99%

“…diseasefree, predator-prey model, are analysed respectively in Sections 3 and 4 . Here we extend the analysis of [8] by a phase portrait analysis to study the total collapse of the system caused by a heteroclinic connection between the two prey-only saddle equilibria.…”

Section: Introductionmentioning

confidence: 99%

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Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

Kooi

Venturino

2016

Mathematical Biosciences

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MSC: Keywords:Herd behavior Disease transmission Ecoepidemics System collapse Local and global bifurcations a b s t r a c tIn this paper we analyse a predator-prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the RosenzweigMacArthur predator-prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator-prey interaction term. The system dynamics is investigated using simulations, classical existence and asymptotic stability analysis and numerical bifurcation analysis. A number of bifurcations, such as transcritical and Hopf bifurcations which occur commonly in predator-prey systems will be found. Because of the square root interaction term there is non-uniqueness of the solution and a singularity where the prey population goes extinct in a finite time. This results in a collapse initiated by extinction of the healthy or susceptible prey and thereafter the other population(s). When also a positive attractor exists this leads to bistability similar to what is found in predator-prey models with a strong Allee effect. For the two-dimensional disease-free (i.e. the purely demographic) system the region in the parameter space where bistability occurs is marked by a global bifurcation. At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al., 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon. Here we extend its analysis using a phase portrait analysis. For the three-dimensional ecoepidemic predator-prey system where the prey is affected by the disease, also tangent bifurcations including a cusp bifurcation and a torus bifurcation of limit cycles occur. This leads to new complex dynamics. Continuation by varying one parameter of the emerging quasi-periodic dynamics from a torus bifurcation can lead to its destruction by a collision with a saddle-cycle. Under other conditions the quasi-periodic dynamics changes gradually in a trajectory that lands on a boundary point where the prey go extinct in finite time after which a total collapse of the three-dimensional system occurs.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

Kooi

Venturino

2016

Mathematical Biosciences

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“…Finally, incorporation of a saturation effect via a HTII response function within a herd behavior ecoepidemic system with infected predators, [54] , gives the model:…”

Section: Herd Behaviormentioning

confidence: 99%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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Abstract. Models proposed for the description of population interactions with pathogenic agents are presented. We review some basic quadratic-interactions models, then move to more complex demographics, structured models, models involving several populations, delays, plankton dynamics, the Allee effect and group behavior. In most of these cases basic reproduction numbers are evaluated and commented.

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A mathematical model for bovine tuberculosis among buffaloes and lions in the Kruger National Park

Assis

Massad

Assis

et al. 2017

Math Methods in App Sciences

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In this paper, a model for the spread of tuberculosis between buffaloes and lions is presented and analyzed. The most important system parameters are identified: vertical and horizontal disease transmission among the buffaloes and the influence of intraspecific competition between healthy and diseased buffaloes on the infected buffaloes population. Removal of diseased prey appears to be the most effective strategy to render the ecosystem disease free.

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Ecoepidemic models with prey group defense and feeding saturation

Cited by 52 publications

References 30 publications

Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

Ecoepidemiology: a More Comprehensive View of Population Interactions

A mathematical model for bovine tuberculosis among buffaloes and lions in the Kruger National Park

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