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A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers’ Migration
Bulletin of Mathematical Biology ( IF 2.0 ) Pub Date : 2020-07-01 , DOI: 10.1007/s11538-020-00764-5
Thibault Moulin 1, 2 , Antoine Perasso 2 , Ezio Venturino 3
Affiliation  

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.

中文翻译:

仅考虑消费者迁徙的草原生态系统元流行病模型

元生态流行模型概括了元种群系统,将当地种群动态与斑块间迁移以及流行病扩散相结合。引入了资源-消费者模型,由两个补丁组成的生态系统,消费者可以在其中自由移动。疾病会影响第二个补丁的资源。这种情况对应于草原草食性环境,其中一个以粗放方式管理的斑块具有更广泛的植物多样性,而另一个斑块则高度施肥,导致重要的牧草生产。后者也受到真菌疾病的影响。食草动物都以健康或受感染的作物为食,并且可以在两个斑块之间自由迁移。初步调查的重点分别是从模型的某些部分出现的行为,由非耦合补丁和纯粹的人口耦合模型形成。整个系统的平衡被评估和表征。然后将结果与纯粹的人口统计模型进行比较,以突出疾病在这种动态中的作用。对该模型的彻底数值研究完成了该分析,以评估每个平衡附近的系统行为。还探索了系统分岔以及系统平衡对参数扰动的响应。在适当的情况下,疾病的根除是可能的。五个种群通过持续振荡共存也是可能的,但不是在一个稳定的水平。然后将结果与纯粹的人口统计模型进行比较,以突出疾病在这种动态中的作用。对该模型的彻底数值研究完成了该分析,以评估每个平衡附近的系统行为。还探索了系统分岔以及系统平衡对参数扰动的响应。在适当的情况下,疾病的根除是可能的。五个种群通过持续振荡共存也是可能的,但不是在一个稳定的水平。然后将结果与纯粹的人口统计模型进行比较,以突出疾病在这种动态中的作用。对该模型的彻底数值研究完成了该分析,以评估每个平衡附近的系统行为。还探索了系统分岔以及系统平衡对参数扰动的响应。在适当的情况下,疾病的根除是可能的。五个种群通过持续振荡共存也是可能的,但不是在一个稳定的水平。在适当的情况下,疾病的根除是可能的。五个种群通过持续振荡共存也是可能的,但不是在一个稳定的水平。在适当的情况下,疾病的根除是可能的。五个种群通过持续振荡共存也是可能的,但不是在一个稳定的水平。
更新日期:2020-07-01
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