Mathematical models of diseases spreading in symbiotic communities

Symbiotic communities are relevant from the biologists' viewpoint. Diseases affecting interacting populations have earlier been considered in ecoepidemic models with interactions of competitive or predational type but also for mutualistic associations. Here the analysis is extended to populations experiencing mutualism, in the more realistic case in which the benefits of the symbiosis cannot exhibit unlimited growth as function of the ecosystem populations. The investigation of some such situations is not only biologically relevant, but it becomes important even from an economic point of view, like for instance the case of chestnut trees affected by chestnut cancer and several mushrooms. We model a symbiotic ecoepidemic system via a dynamical system, assuming that the return coming from positive species interactions has an upper bound. We matematically analyze its long-term behavior and identify conditions leading to disease eradication. Some new features characteristic of these models with respect to earlier ecoepidemic models with different underlying demographics are highlighted.