a b s t r a c tIn this paper, we show that under suitable simple assumptions the classical two populations system may exhibit unexpected behaviors. Considering a more elaborated social model, in which the individuals of one population gather together in herds, while the other one shows a more individualistic behavior, we model the fact that interactions among the two occur mainly through the perimeter of the herd. We account for all types of populations' interactions, symbiosis, competition and the predator-prey interactions. There is a situation in which competitive exclusion does not hold: the socialized herd behavior prevents the competing individualistic population from becoming extinct. For the predator-prey case, sustained limit cycles are possible, the existence of Hopf bifurcations representing a distinctive feature of this model compared with other classical predator-prey models. The system's behavior is fully captured by just one suitably introduced new threshold parameter, defined in terms of the original model parameters.

We mathematically investigate the effects of a disease which is spread in an interacting population system by the action of an external carrier.