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Disease Spread among Hunted and Retaliating Herding Prey

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  • Ezio Venturino

    (Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
    Member of the INdAM research group GNCS.)

Abstract

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.

Suggested Citation

  • Ezio Venturino, 2022. "Disease Spread among Hunted and Retaliating Herding Prey," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4397-:d:979977
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    References listed on IDEAS

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    3. Djilali, Salih, 2019. "Impact of prey herd shape on the predator-prey interaction," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 139-148.
    4. Bulai, Iulia Martina & Venturino, Ezio, 2017. "Shape effects on herd behavior in ecological interacting population models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 40-55.
    5. Cecilia Berardo & Iulia Martina Bulai & Ezio Venturino, 2021. "Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators," Mathematics, MDPI, vol. 9(20), pages 1-18, October.
    6. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
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