Z-type control methods for ecological and ecoepidemiological models with invasive prey

The process by which nature and evolution discriminate between species bound to survive or become extinct has always been an interesting phenomenon. One example of this selection is represented by biological invasions, when alien species spread into new environments causing ecological disruptions, alteration of native population dynamics and ecosystem dysfunctioning. In this work, the focus is placed on the introdution of the Eastern Cottontail (Sylvilagus floridanus) into Northern and Central Italy regions and on its consequences with the native ecosystem. Specifically, this has influenced the local predator-prey dynamics of the indigenous European hares (Lepus europaeus) and foxes (Vulpes vulpes), consequently producing a ``hyperpredation'' effect on hares. In the literature such an event has already been studied by Caudera et al. who validated this trend comparing the theoretical results with the ones collected from field studies. In addition to this scenario, if the invasive species is carrier of a certain disease, its introduction into a healthy and uncontaminated territory can be the cause of an epidemic spread among the native populations. Although not yet supported by field data, a likely situation has been modeled, where the viral European brown hare syndrom (EBHS) epidemic has been hypothesized, as both cottontails and hares exhibit susceptibility to infection. Exploring this theme, the objective of the framework is the employment of Z-control techniques with the aim of mitigating the negative effects of the invasion. Particularly, the Z-control method is applied in order to drive chosen populations toward a desired state that can ensure survival of native species and/or eradication of the disease at least theoretically.