A More Realistic Formulation of Herd Behavior for Interacting Populations

Borgogni, Daniele; Losero, L.; Venturino, Ezio

doi:10.1007/978-3-030-46306-9_2

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…However, variants of this assumption have been already studied [13,14], possibly accounting for fish schools and insect swarms living in a three-dimensional environment or for planar shapes that are not smooth or even become fractals. Further, the response function has also been modified to render it more realistic at low population values or to allow generic formulations that are not necessarily tied to a specific mathematical form [15,16].…”

Section: Introductionmentioning

confidence: 99%

Disease Spread among Hunted and Retaliating Herding Prey

Venturino

2022

Mathematics

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Two new ecoepidemic models of predator–prey type are introduced. They feature prey that gather in herds. The specific novelty consists of the fact that the prey also has the ability to defend themselves if they are in large numbers. The two deterministic models differ in the way a disease spreading among the ecosystem is transmitted, either by direct contact among infected and susceptible animals or by the intake of a virus present in the environment. Only the disease-free and the endemic equilibrium are allowed, and they are analyzed for feasibility and stability. The boundedness results allow us to gather some results regarding global stability. Persistent oscillations can be triggered when some relevant model parameters cross specific thresholds, causing repeated epidemic outbreaks. Furthermore, the environmental contamination through a free viruses destabilizes the endemic equilibrium and may lead to large amplitude oscillations, which are dangerous because they are potentially harmful to ecosystems. The bifurcation parameters leading to the limit cycle onset are related to the epidemics. For instance, they could be the disease-related mortality and the transmission rates, whether by direct contact among individuals or through the environment. The results of this investigation may provide insights to theoretical ecologists and may provide useful indications for epidemic spread containment.

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Section: Introductionmentioning

confidence: 99%

Disease Spread among Hunted and Retaliating Herding Prey

Venturino

2022

Mathematics

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Multiple Predation on Prey Herding and Counteracting the Hunting

Bondi,

Ferri,

Giordanengo

et al. 2023

Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

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On Some Methodological Issues in Mathematical Modeling of Interacting Populations

et al. 2023

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In this paper, we focus on some important aspects of model building. The discussion specifically concerns the case of predator–prey interactions. We introduce here two models whose slight difference lies just in the way predators survive. In the former, they are taken to feed only on the modeled prey, i.e., to be specialists; in the second one, they are generalists, i.e., they can survive on other not explicitly modeled food resources. But our main focus is on the prey, that may disappear due to the Allee effect, if reduced to very low numbers. On the other hand, they also exhibit herd behavior. Our main aim is the discussion of the issues of mathematical modeling of such situation. We show on this example that modeling requires much more than equations patching from different systems. The analysis of the models indicates that the ecosystem may collapse in the case of specialist predators. If the predators have other feeding resources, they instead can thrive. Both types of models exhibit bistability between the prey-free state and coexistence.

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A More Realistic Formulation of Herd Behavior for Interacting Populations

Cited by 3 publications

References 21 publications

Disease Spread among Hunted and Retaliating Herding Prey

Disease Spread among Hunted and Retaliating Herding Prey

Multiple Predation on Prey Herding and Counteracting the Hunting

On Some Methodological Issues in Mathematical Modeling of Interacting Populations

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