Z-Type Control Methods on a Three-Species Model with an 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 paper, we concentrate on the introduction of the Eastern cottontail ( Sylvilagus floridanus ) into the regions of northern and central Italy. This has influenced the local predator–prey dynamics of the indigenous European hares ( Lepus europaeus ) and red foxes ( Vulpes vulpes ), consequently producing a “hyperpredation” effect on hares. In this framework, we investigate this scenario with the objective of mitigating the negative effects of the invasion. Specifically, we devise and apply a Z-control technique in order to drive chosen populations toward a desired state that at least theoretically can ensure the survival of native species. The purpose of such a study is twofold: on one hand, this approach is employed with the aim of reducing the invasive population; secondly, it aims to avoid the extinction of native prey, i.e., the hare population.