Optimal Control to Limit the Propagation Effect of a Virus Outbreak on a Network

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

Analysis, Simulation and Control of a New Measles Epidemic Model

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

State Feedback Optimal Control with Singular Solution for a Class of Nonlinear Dynamics

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

An Improvement in a Local Observer Design for Optimal State Feedback Control: The Case Study of HIV/AIDS Diffusion

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 on

A linear quadratic regulator for nonlinear SIRC epidemic model

The control of an epidemic disease consists in introducing the strategies able to reduce the number of infected subjects by means of medication/quarantine actions, and the number of the subjects that could catch the disease through an informative campaign and, when available, a vaccination strategy. Some diseases, like the influenza, do not guarantee immunity; therefore, the subjects could get ill again by different strain of the same viral subtype. The epidemic model adopted in this paper introduces the cross-immune individuals; it is known in literature as SIRC model, since the classes of susceptible (S), infected (I), removed (R) and cross-immune (C) subjects are considered. Its control is herein determined in the framework of the linear quadratic regulator, by applying to the original nonlinear model the optimal control found on the linearized system. The results appear satisfactory, and the drawback of using a control law based on the linear approximation of the system is compensated by the advantages arising from such a solution: no costate equations to be solved and a solution depending on the current state evolution which allows a feedback implementation

Mobile sensors networks under communication constraints

The paper deals with the problem of computing optimal or suboptimal motion for a network of mobile sensors. The use of moving sensors means that for each point of the field under measurement asynchronous discrete time measures are given instead of continuous time ones, being possible to fix in advance the maximum time interval between two consecutive measures for the same point. The constraints here considered are on the full coverage of the fleld, with respect to the measurements, within the prefixed time interval and on the communication connections, between any pair of moving sensors, at any time. A solution, based on a local distributed approach, is proposed and compared with a centralized approach previously proposed, and here recalled, by the same authors. Some simulations show the effectiveness of the both solutions, putting in evidence advantages, disadvantages and differences

Early estimation of the number of hidden HIV infected subjects: An extended Kalman filter approach

In the last decades several epidemic emergencies have been affecting the world, influ encing the social relationships, the economics and the habits. In particular, starting in the early 0 80, the Acquired Immunodeficiency Syndrome, AIDS, is representing one of the most worrying sanitary emergency, that has caused up to now more than 25 million of dead patients. The infection is caused by the Human Immunodeficiency Virus, HIV, that may be transmitted by body fluids; therefore with wise behaviours the epidemic spread could rapidly be contained. This sanitary emergency is peculiar for the long incubation time: it can reach even 10 years, a long period in which the individual can unconsciously infect other subjects. The identification of the number of infected unaware people, mandatory to define suitable containment measures, is here obtained by using the extended Kalman filter applied to a noisy model in which, reasonably, only the number of infected diagnosed patients is available. Numerical simulations and real data analysis support the effective ness of the approac

Recursive Least Squares Filtering Algorithms for On-Line Viscoelastic Characterization of Biosamples

The mechanical characterization of biological samples is a fundamental issue in biology and related fields, such as tissue and cell mechanics, regenerative medicine and diagnosis of diseases. In this paper, a novel approach for the identification of the stiffness and damping coefficients of biosamples is introduced. According to the proposed method, a MEMS-based microgripper in operational condition is used as a measurement tool. The mechanical model describing the dynamics of the gripper-sample system considers the pseudo-rigid body model for the microgripper, and the Kelvin–Voigt constitutive law of viscoelasticity for the sample. Then, two algorithms based on recursive least square (RLS) methods are implemented for the estimation of the mechanical coefficients, that are the forgetting factor based RLS and the normalised gradient based RLS algorithms. Numerical simulations are performed to verify the effectiveness of the proposed approach. Results confirm the feasibility of the method that enables the ability to perform simultaneously two tasks: sample manipulation and parameters identification