Ricerc@Sapienza

The paper deals with the modelling and the control of a job market dynamics which considers unemployed individuals and two classes of jobs: a temporary one, characterised by a lower quality of economical treatment and/or long duration assurance for the workers, and a regular one, more stable and economically more satisfactory. For each of the two classes, the active workers as well as the vacancies are considered. Control actions are introduced, representing different government efforts devoted to the quantity and the quality improvements of the work.

The hepatitis B virus (HBV) infection represents
a global health problem; it can be transmitted through contact
with infected blood or other body fluids and it is dangerous
being highly contagious. Hepatitis B is preventable with effective
vaccine, as it is strongly recommended by the World
Health Organization; its protection is possibly life-long, at least
20 years. Mathematical modelling is a useful tool to study the
evolution of an epidemic spread and possibly to suggest suitable

The aim of this paper is to propose an optimal control strategy to face the propagation effects of a virus
outbreak on a network; a recently proposed model is integrated and analysed. Depending on the specific
model caracteristics, the epidemic spread could be more or less dangerous leading to a virus free or to a virus
equilibrium. Two possible controls are introduced: a test on the computers connected in a network and the
antivirus. In a condition of limited resources the best allocation strategy should allow to reduce the spread of

In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model
is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible,
the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories
are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an
additional complication, not risky by itself but dangerous if caught togeter with the measles. These two

The paper addresses the problem of an observer design for a nonlinear system for which a preliminary linear
state feedback is designed but the full state is not measurable. Since a linear control assures the fulfilment of
local approximated conditions, usually a linear observer is designed in these cases to estimate the state with
estimation error locally convergent to zero. The case in which the control contains an external reference, like
in regulations problems, is studied, showing that the solution obtained working with the linear approximation

The paper addresses the problem of human virus spread reduction when the resources
for the control actions are somehow limited. This kind of problem can be successfully solved in the
framework of the optimal control theory, where the best solution, which minimizes a cost function
while satisfying input constraints, can be provided. The problem is formulated in this contest for the
case of the HIV/AIDS virus, making use of a model that considers two classes of susceptible subjects,

Mathematical modeling represents a useful instrument to describe epidemic spread
and to propose useful control actions, such as vaccination scheduling, quarantine, informative
campaign, and therapy, especially in the realistic hypothesis of resources limitations. Moreover, the
same representation could efficiently describe different epidemic scenarios, involving, for example,
computer viruses spreading in the network. In this paper, a new model describing an infectious

The analysis of singular solutions in optimal control problems is addressed. The case of systems with two inputs is investigated characterising all the possible combination of singular arcs and constant boundary values. It is described the extension to a two input system of a previously proposed procedure for computing the control along the singular arcs in a state feedback form for one input dynamics. The procedure makes use of the possibility of computation in an analytical form of the costate as a function of the state.

In this chapter the problem of the interaction between groups of subjects singularly characterized by a specific infectious disease is addressed.

The paper studies the problem of determining the optimal control when singular arcs are present in the solution. In the general classical approach, the expressions obtained depend on the state and the costate variables at the same time, so requiring a forward-backward integration for the computation of the control. In this paper, firstly sufficient conditions on the dynamics structure are discussed, in order to have both the control and the switching function depending on the state only, computable by a simple forward integration.