One of the emergencies related to climate change concerns the spread of epidemics; even in areas not linked to a humid-tropical climate, Dengue, West Nile, Zika are spreading, to name the most common. Possible containment measures are linked to human behavior, such as the use of appropriate clothing, mosquito nets, repellents. Other measures concern actions to limit the reproduction of mosquitoes, for example avoiding stagnant water, and, in some cases, they are more invasive, such as acting with targeted disinfestations. The combined action of these strategies, taking into account the limitations related to their applicability and the protection of the ecosystem, is implemented in this work, within the framework of the optimal control theory. The proposed results underline the importance of prevention action and propose suggestions on how to implement the most invasive actions.

In the present paper, the effectiveness of the use of Machine Learning techniques, in particular Deep Learning algorithms, in the analysis of Ti-6Al-4V (Ti64) manufacture is studied; relationships between the values of physical parameters used during the production and mechanical characteristics are defined by means of the analysis of images taken from sections of the specimens, where defects and microstructural discontinuities can be observed. The Deep Learning approach, widely used for image classification and features extraction, also in this case shows promising possibilities, as proved by the implementation results reported.

In the paper, the problem of the interaction between two separated population is considered when an infectious disease is presented. An asymmetric behaviour is studied, with one smaller population receiving a people flow from a second more numerous one. For each of them, the different conditions with respect to the epidemic status are considered as well as different numbers of flowing individuals. The reference case in mind is the possible COVID-19 epidemic during the next Jubilee 2025, where a very large amount of pilgrims are expected to come in Italy and, mainly, in Rome, with numbers comparable with the usual living population. A theorical study about the effects on the equilibria conditions, completed with a numerical analysis of different possible scenarios, is reported in the paper, showing that it must be expected a sensible increment of the number of infected individuals.

The problem of the definition of a mathematical model for epidemics, where the virus transmission is op erated by an infected vector like an insect, is addressed. Through the consideration of a small number of compartments, in order to keep the mathematical analysis affordable, a five dimensional model is proposed and, successively, used for the analysis of the main characteristics of the disease. Closed form expression are then obtained for the equilibria, the stabiliy conditions and the reproduction number. Some numerical results referring to the dengue disease emergency are also presented, firstly to identify the unknown model parameters and then to validate the effectiveness of the model itself. Using such a model, some considerations on the most effective action lines for spidemic containment are discussed.

Measles is one of the most dangerous epidemic disease for its high reproduction number and the possible complications on already weakened patients. Effective vaccination is available since the early 60s and a suit able vaccination campaign could interrupt this epidemic disease. The most common approach for the disease description considers compartmental models, effective but requiring the identification of model parameters, generally data consuming. A different approach is data driven, that is it consideres autoregressive modeling with exogenous input. The autoregressive modeling is here considered describing measles evolution by using measurable available information, like the number of infected patients and the percentage of vaccinated indi viduals. A penalized control is herein determined, thus taking into account also limitation in control actions. Numerical results, based on available real data, show the effectivenes of the approach.

The study of Human Immunodeficiency Virus (HIV) and of its progression to Acquired Immune Deficiency Syndrome (AIDS) has been a challenge by scientists since the early 1980s; the improvements in the knowledge of its transmission and of the evolution of the disease have strongly reduced the mortality, even if up to know an effective vaccine is not available. Nevertheless, the Highly Active Antiretroviral Therapy (HAART) allows a high life expectancy. Some of the mechanisms of HIV reproduction are under investigation and recent observations are suggesting the existence of virus reservoir in the brain, the liver, the lungs and the gut. In particular, due to untreated amounts of virus, neurocognitive disorders as well as motor nerves diseases and weakness in muscles are improved in patients already weakened. In this paper it is considered a mathematical modelling to study the within-host viral dynamics, analysing the dynamics of the CD4-T cells, of the macrophages both inside and outside the brain, uninfected and infected, along with the virions carrying on the infection. An optimal control strategy is proposed and implemented,aiming at maximizing the number of healthy cells, while reducing the number of infected ones, scheduling suitably the therapy.

An advanced Fuzzy Logic Controller (FLC) that considers all the states of the brain tumor system is designed for the chemotherapy treatment. A Mamdani-type FLC is proposed for dynamically controlling the chemotherapy drug for the tumor system; the chemotherapy treatment of brain tumors requires advanced strategies which mainly depend upon the severity of the tumor. In this work, the advanced FLC designed aims both at determining the amount of chemotherapy to eliminate tumor cells, and at preserving the minimum amount of healthy and immune cells. The controller's performance is verified using MATLAB software based on different control parameters, showing its effectiveness in reducing the tumor cells. It has shown favorable results in terms of steady-state error, rate of convergence, and amount of drug consumed.

The breast cancer represents one of the most frequent disease diagnosed worldwide; with the modern im- provements in medicine and technology a fast detection of tumor could allow a total recovery. In this paper, it is proposed a compartmental epidemiological model in which the female population is partitioned depend- ing on the condition with respect to the tumor diagnosis. The model is identified referring to the population of a region of Italy, using real data; increasing levels of control are introduced, from noninvasive prevention to combination of surgery and chemotherapy. In the framework of optimal control, aiming at reducing the number of severe cases and of women dead by tumor, a suitable combination of control effort is determined, considering constraints in the containment measures. Numerical results stress the importance of prevention that at the very beginning increases the number of discovered positive diagnosis, and, successively, signifi- cantly contains the fatal consequences of breast cancer on the population by reducing the late diagnosis.

In the paper an optimal control solution is provided for the containment of the number of infected individuals in COVID-19 pandemic under vaccination campaign. The possibility to dynamically change the cost of the controls according to the ongoing evolution within the design procedure allows to get great efforts in presence of very serious disease conditions, saving resources otherwise. The different contribution of vaccinated and unvaccinated individuals to the epidemic spread is investigated, optimising the controls which describe the individual contact restrictions separately for the two classes and showing that it would have been possible to reduce all the social limitations introduced by many governments for the vaccinated individuals since the beginning of the vaccination campaign.

The COVID-19 pandemic highlighted the fragility of the world in addressing a global health threat. The available resources of the pre-pandemic national health systems were inadequate to cope with the huge number of infected subjects needing health care and with the rapidity of the infection spread characterizing the COVID-19 outbreak. Indeed, an adequate allocation of the resources could produce in principle a strong reduction of the infection spread and of the hospital burden, preventing the collapse of the health system. In this work, taking inspiration from the COVID-19 and the difficulties in facing the emergency, an optimal problem of resource allocation is formulated on the basis of an ODE multi-group model composed by a network of SEIR-like submodels. The multi-group structure allows to differentiate the epidemic response of different populations or of various subgroups in the same population. In fact, an epidemic does not affect all populations in the same way, and even within the same population there can be epidemiological differences, like the susceptibility to the virus, the level of infectivity of the infectious subjects and the recovery from the disease. The subgroups are selected within the total population based on some peculiar characteristics, like for instance age, work, social condition, geographical position, etc., and they are connected by a network of contacts that allows the virus circulation within and among the groups. The proposed optimal control problem aims at defining a suitable monitoring campaign that is able to optimally allocate the number of swab tests between the subgroups of the population in order to reduce the number of infected patients (especially the most fragile ones) so reducing the epidemic impact on the health system. The proposed monitoring strategy can be applied both during the most critical phases of the emergency and in endemic conditions, when an active surveillance could be crucial for preventing the contagion rise.

Since the beginning of 2020 in few weeks all the world has been interested by the pandemic due to SARSCoV 2, causing more than 3 millions of dead people and more than 146 millions of infected patients. The virus moves with people and the most effective containment measure appears to be the severe lockdown; on the other hand, for obvious social and economic reasons, it can not be applied for long periods. Moreover, the increasing knwoledge on the virus and on its trasmission modes suggested various strategies, such as the use of masks, social distancing, disinfection and the fast identification of infected patients, up to the recent vaccination campaign. In this paper, the COVID-19 spread is studied referring to the Italian situation; the control actions introduced during 2020-2021 are identified in terms of their actual effects, allowing to study possible intervention scenarios.

The paper aims at a discussion of the effects of the containment measures against COVID-19 through the analysis of the reproduction number. Starting from a mathematical model in which several controls are considered, including the vaccination, and introducing also an hypotised limited duration of the immunity acquired both from vaccine and from healing from the illness, the steady state behaviour, both in the uncontrolled and in the controled cases is studied. The expressions for the basic reproduction number and the actual reproduction number under control actions are computed by means of the next generation matrix approach. This function is numerically investigated, showing some graphs which illustrate, qualitatively and quantitatively, in an intuitive way the positive effects of the controls and the negative contribution of the absence of a lifetime immunization from virus.

The present work deals with an Ordinary Differential Equation (ODE) model specifically designed to describe the COVID-19 evolution in Italy. The model is particularised on the basis of National data about the infection status of the Italian population to obtain numerical solutions that effectively reproduce the real data. Our epidemic model is a classical SEIR model that incorporates two compartments of infected subpopulations, representing diagnosed and undiagnosed individuals respectively, and an additional quarantine compartment. Possible control actions representing social, political, and medical interventions are also included. The numerical results of the proposed model identification by least square fitting are analysed and commented with special emphasis on the estimation of the number of asymptomatic infective individuals. Our fitting results are in good agreement with the epidemiological data. Short and long-term predictions on the evolution of the disease are also given.

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 to get local solutions produces non consistent results in terms of local regions of convergence for the system and for the observer. A solution to this problem is provided, proposing a different choice for the observer design which allows to obtain all conditions locally satisfied on the same local region in the neighbourhood of a new equilibrium point. The case study of an epidemic spread control is used to show the effectiveness of the procedure. The linear control with regulation term is present in this case because the problem is reconducted to a Linear Quadratic Regulation problem. Simulation results show the differences between the two approaches and the effectiveness of the proposed one

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 the virus as soon as possible.

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 novelties are taken into account in designing and scheduling suitably control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of the model is developed and the optimal control strategies are compared with other not optimized actions. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society when an epidemic spread occurs, such as the quarantine intervention.

In this paper, a new model describing the human immunodeficiency virus (HIV)-acquired immuno deficiency syndrome (AIDS) epidemic spread is proposed. The improvement with respect to the known models has been driven by recent results obtained from historical data collection and the suggestions given by the World Health Organization: the characteristics of the virus diffusion, mainly by body fluids, imply the trivial fact that wise behaviors of healthy subjects and fast timely recognition of a new positive diagnosis should reduce the spread quite fast. Therefore, the set of susceptible subjects is divided into two categories: the wise people that, suitably informed, avoid dangerous behaviors, and the ones that, with irresponsible acts, could get the infection. The set of infected subjects is constituted by people who are still not aware of being infected (and therefore are responsible of the HIV spread), along with the subjects aware of being infected by HIV or AIDS. Inspired by the international guidelines suggestions, three controls are introduced, aiming both at the prevention and at the cure: an informative campaign, a test campaign, and an HIV/AIDS therapy action. Among them, the core of the control effort is a fast HIV diagnosis. The equilibrium points, their stability, and the influences of the introduced inputs to the system behavior are studied, yielding to preliminary statements for prospective works on suitable control design approaches.

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, sufficient conditions on the dynamics structure are provided and discussed in order to have both the control and the switching function depending on the state only, so simplifying the computation avoiding the necessity of the backward integration. The approach has been validated on a classical SIR epidemic model.

In this paper, the problem of optimal resource allocation depending on the system evolution is faced. A preliminary analysis defines the global effort required in any subset of the system state space according to needed or desired goals. Then, in the definition of the cost function, the control action is weighted by a piecewise constant function of the state, whose different constant values are defined for each subset previously defined. The aim is to weight the control according to the distinct conditions, so getting different solutions in each state space region so to optimize the planned resources according to the global goal. A constructive algorithm to compute iteratively the final control law is outlined. The effectiveness of the proposed approach is tested on a typical model of human immunodeficiency virus (HIV) present in literature

The aim of this paper is to propose a real-time classification algorithm for the low-amplitude electroencephalography (EEG) signals, such as those produced by remembering an unpleasant odor, to drive a brain-computer interface. The peculiarity of these EEG signals is that they require ad hoc signals preprocessing by wavelet decomposition, and the definition of a set of features able to characterize the signals and to discriminate among different conditions. The proposed method is completely parameterized, aiming at a multiclass classification and it might be considered in the framework of machine learning. It is a two stages algorithm. The first stage is offline and it is devoted to the determination of a suitable set of features and to the training of a classifier. The second stage, the real-time one, is to test the proposed method on new data. In order to avoid redundancy in the set of features, the principal components analysis is adapted to the specific EEG signal characteristics and it is applied; the classification is performed through the support vector machine. Experimental tests on ten subjects, demonstrating the good performance of the algorithm in terms of both accuracy and efficiency, are also reported and discussed.

In this paper we present an integrated approach to COSMO-SkyMed image analysis and classification exploiting integration of different data of the regions of interest, namely urban forestry areas, wide urban parks. The aim is to provide a methodology for exploiting complex data structures built upon multi resolution grids gathering together with optical and X-SAR images, also historical land exploitation and meteorological data, records of human habits, and several other information sources. Although these data are specifically gathered to built a fire susceptibility map, the method is quite general. Indeed, the contribution of the model and its novelty relies manly on the definition of a learning schema lifting different factors and aspects of the event to be identified (here fire causes), including physical, social and behavioral ones, to the design of a fire susceptibility map, of a specific urban forestry. The outcome is an integrated geospatial database providing an infrastructure that merges cartography, heterogeneous data and complex analysis, in so establishing a digital environment where users and tools are interactively connected in an efficient and flexible way.

We present a method for an on-line traffic optimal estimation on a communication link. The proposed filtering procedure is based on a traffic model consisting of a birth-and-death process, elaborates the current noisy measurements from the link and minimizes the estimation error conditional variance. Performance of the method is tested by considering both simulated and real data. This result is of interest with reference to a possible procedure for bandwidth allocation in the framework of bandwidth brokers. The bandwidth allocation is necessary to provide quality of service guarantees to users and requires, as a preliminary step, on-line traffic estimation.

The aim of this paper is to provide a theoretical set up and a mathematical model for the problem of image reconstruction. The original image belongs to a family of two-dimensional (2-D) possibly discontinuous functions, but is blurred by a Gaussian point spread function introduced by the measurement device. In addition, the blurred image is corrupted by an additive noise. We propose a preprocessing of data which enhances the contribution of the signal discontinuous component over that one of the regular part, while damping down the effect of noise. In particular we suggest to convolute data with a kernel defined as the second order derivative of a Gaussian spread function. Finally, the image reconstruction is embedded in an optimal problem framework. Now convexity and compactness properties for the admissible set play a fundamental role. We provide an instance of a class of admissible sets which is relevant from an application point of view while featuring the desired properties.