A Minimal Model for Ecoepidemics With Group Defense

Abstract

The new idea of group defense as recently introduced by the author in the context of two interacting populations is in this paper applied to communities subject also to a disease. The system is formulated with the bare minimum of interactions among all the populations involved in order to highlight the effects of the nonlinearity describing the defense mechanism. A key parameter identified in the purely demographic model, which completely describes its outcomes, is seen here to have an important role also, in that its dropping below a threshold prevents the disease from invading the environment and causes the healthy prey and predators to coexist via persistent oscillations.

Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

“…We consider the model presented in [23] , which we briefly illustrate again here for the convenience of the reader, to better emphasize the changes in that main model. The basic ecological model is an adapted Rosenzweig-MacArthur model first discussed in [19] where both prey and predators have an homogeneous spatial distribution.…”

“…The prey gather together in herds where only prey individuals that live close to the herds boundary on the ground are subject to hunting by predators. In [1,5,23,25] this feature has been taken into account in ecoepidemiological systems. These, besides ecological situations dealing with demographically interacting populations, consider also a transmissible disease in the system, see [16,24] for an introductory account.…”

Ecoepidemic models with prey group defense and feeding saturation

“…In the context of predators' behavior see also related concepts in (Cosner et al, 1999). Ecological Complexity 22 (2015) [50][51][52][53][54][55][56][57][58] The combination of both the above ideas, namely disease affecting interacting populations and herd behavior, has been explored first in (Venturino, 2011), a study in which the epidemic is assumed to affect the prey, and then in (Belvisi and Venturino, 2013), for the case of diseased predators. In plankton dynamics, this idea has been explored in (Chattopadhyay et al, 2008;Romano et al, 2014), where it is assumed that toxic phytoplankton agglomerates in patches and releases poison through their surface.…”

Ecoepidemiology: a More Comprehensive View of Population Interactions

“…These concepts are extended to the ecoepidemic case in [136]. Denoting by S the healthy prey, by I the infected prey and by Z the predators' population, assuming that the diseased individuals are left behind and therefore are still subject to individual attacks, the system is:…”