Using remote sensing data within an optimal spatiotemporal model for invasive plant management: the case of Ailanthus altissima in the Alta Murgia National Park.

We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction-diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density.

Using awareness to Z-control a SEIR model with overexposure: Insights on Covid-19 pandemic.

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease.

On the Z-type control of backward bifurcations in epidemic models.

We investigate how the Z-type dynamic approach can be applied to control backward bifurcation phenomena in epidemic models. Because of its rich phenomenology, that includes stationary or oscillatory subcritical persistence of the disease, we consider the SIR model introduced by Zhou & Fan in [Nonlinear Analysis: Real World Applications, 13(1), 312-324, 2012] and apply the Z-control approach in the specific case of indirect control of the infective population. We derive the associated Z-controlled model both when the desired Z-controlled equilibrium is an endemic equilibrium with a very low number of infectives and when the Z-controlled equilibrium is a disease-free equilibrium.

Personalizing physical exercise in a computational model of fuel homeostasis.

The beneficial effects of physical activity for the prevention and management of several chronic diseases are widely recognized. Mathematical modeling of the effects of physical exercise in body metabolism and in particular its influence on the control of glucose homeostasis is of primary importance in the development of eHealth monitoring devices for a personalized medicine. Nonetheless, to date only a few mathematical models have been aiming at this specific purpose.

On the dynamics of a generalized predator-prey system with Z-type control.

We apply the Z-control approach to a generalized predator-prey system and consider the specific case of indirect control of the prey population. We derive the associated Z-controlled model and investigate its properties from the point of view of the dynamical systems theory. The key role of the design parameter λ for the successful application of the method is stressed and related to specific dynamical properties of the Z-controlled model.