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A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers’ Migration

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Abstract

Metaecoepidemic models generalize metapopulation systems, combining local population dynamics with inter-patch migration coupled with an epidemic proliferation. A resource–consumer model is introduced with an ecosystem composed by two patches, in which consumers can freely move. A disease affects resources of the second patch. This situation corresponds to a grassland–herbivore environment, where one patch, managed in an extensive way, has a wider plant diversity, while the other one is highly fertilized leading to an important forage production. The latter is also subject to a fungal disease. Herbivores both feed on healthy or infected crop and can freely migrate between the two patches. A preliminary investigation focuses on behaviors emerging from some parts of the model, respectively, formed by uncoupled patches and by the purely demographic coupled model. Equilibria of the whole system are assessed and characterized. Results are then compared with the purely demographic model to highlight the role of the disease in this dynamics. A thorough numerical investigation of the model completes this analysis to assess the system behavior near each equilibrium. System bifurcations have also been explored as well as the response of the system equilibria to parameter perturbations. The disease eradication is possible under suitable circumstances. Coexistence of the five populations through persistent oscillations is also possible, but it is not at a stable level.

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Acknowledgements

This research was undertaken within the framework of the Epimath project, funded by Region Bourgogne Franche-Comté.

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Authors and Affiliations

  1. Agroscope, Agroecology and Environment, Reckenholzstrasse 191, 8046, Zurich, Switzerland

    Thibault Moulin

  2. Laboratoire Chrono-environnement, Université Franche-Comté, 16 route de Gray, 25030, Besançon cedex, France

    Thibault Moulin & Antoine Perasso

  3. Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, via Carlo Alberto 10, 10123, Turin, Italy

    Ezio Venturino

Authors
  1. Thibault Moulin
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  2. Antoine Perasso
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  3. Ezio Venturino
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Correspondence to Thibault Moulin.

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Ezio Venturino–Member of the research group GNCS.

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Moulin, T., Perasso, A. & Venturino, E. A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers’ Migration. Bull Math Biol 82, 88 (2020). https://doi.org/10.1007/s11538-020-00764-5

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