Modeling the herd prey response to individualistic predators attacks

In this paper, we consider predators hunting on prey gathered in groups and in such way exhibiting the possibility of reducing the predators pressure. To model this feature, however, we depart from the Holling type II (HTII) response function, in that we assume that a sufficiently large set of prey could respond to individualistic attacks and therefore induce the predator to renounce. The basic idea is described at first in a simple two-populations predator-prey system. It is then expanded considering the generalist predators to deal with two prey. In the first case, both are gathered in herds, and in the second one, one of the two instead behaves individualistically. The net outcome is an enhanced survival for the prey with respect to both the herding cases without and with predators feeding satiation (i.e., using the HTII response)

Predator's alternative food sources do not support ecoepidemics with two-strains-diseased prey

An ecoepidemic model is presented, in which two diseases affect the prey. Predators are allowed to have other food sources. Equilibria are analyzed for feasibility and stability. The most striking result is that in these conditions the two strains cannot both survive in the system, contrary to what is possible to obtain, under suitable assumptions, in standard epidemic models

A minimal model coupling communicable and non-communicable diseases

This work presents a model combining the simplest communicable and non-communicable disease models. The latter is, by far, the leading cause of sickness and death in the World, and introduces basal heterogeneity in populations where communicable diseases evolve. The model can be interpreted as a risk-structured model, another way of accounting for population heterogeneity. Our results show that considering the non-communicable disease (in the end, heterogeneous populations) allows the communicable disease to become endemic even if the basic reproduction number is less than $1$. This feature is known as subcritical bifurcation. Furthermore, ignoring the non-communicable disease dynamics results in overestimating the reproduction number and, thus, giving wrong information about the actual number of infected individuals. We calculate sensitivity indices and derive interesting epidemic-control information.Comment: 19 pages, 5 figure