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

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

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

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

3D beam-column finite element under non-uniform shear stress distribution due to shear and torsion

The paper discusses the application of a 2-node, three-dimensional (3D) beam-column finite element with an enhanced fiber cross-section model to the inelastic response analysis of concrete members. The element accounts for the local distribution of strains and stresses under the coupling of axial, flexural, shear, and torsional effects with an enriched kinematic description that accounts for the out-of-plane deformations of the cross-section. To this end the warping displacements are interpolated with the addition of a variable number of local degrees of freedom. The material response is governed by a 3D nonlinear stress-strain relation with damage that describes the degrading mechanisms of typical engineering materials under the coupling of normal and shear stresses. The element formulation is validated by comparing the numerical results with measured data from the response of two prismatic concrete beams under torsional loading and with standard beam formulations

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

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

Relationship between pulmonary exacerbations and daily physical activity in adults with cystic fibrosis

The aim of this study was to examine the relationship between pulmonary exacerbations and physical activity (PA) in adults with cystic fibrosis (CF)

An Optimal Control Problem Formulation for a State Dependent Resource Allocation Strategy

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Cytoreduction and HIPEC in the treatment of "unconventional" secondary peritoneal carcinomatosis

BACKGROUND: Peritoneal metastasis (PM) is considered a terminal and incurable disease. In the last 30 years, cytoreductive surgery (CRS) and hyperthermic intraperitoneal chemotherapy (HIPEC) radically changed the therapeutic approach for these patients and is regarded as the standard of care for pseudomyxoma peritonei from appendiceal cancer and peritoneal mesotheliomas. Improved survival has also been reported in treating PM from ovarian, gastric, and colorectal cancers. However, PM often seriously complicates the clinical course of patients with other primary digestive and non-digestive cancers. There is increasing literature evidence that helped to identify not only the primary tumors for which CRS and HIPEC showed a survival advantage but also the patients who may benefit form this treatment modality for the potential lethal complications. Our goal is to report our experience with cytoreduction and HIPEC in patients with PM from rare or unusual primary tumors, discussing possible "unconventional" indications, outcome, and the peculiar issues related to each tumor. METHODS: From a series of 253 consecutive patients with a diagnosis of peritoneal carcinomatosis and treated by CRS and HIPEC, we selected only those with secondary peritoneal carcinomatosis from rare or unusual primary tumors, excluding pseudomyxoma peritonei, peritoneal mesotheliomas, ovarian, gastric, and colorectal cancers. Complications and adverse effects were graded from 0 to 5 according to the WHO Common Toxicity Criteria for Adverse Events (CTCAE). Survival was expressed as mean and median. RESULTS: We admitted and treated by CRS and HIPEC 28 patients with secondary peritoneal carcinomatosis from rare or unusual primary tumors. Morbidity and mortality rates were in line with those reported for similar procedures. Median survival for the study group was 56 months, and 5-year overall survival reached 40.3 %, with a difference between patients with no (CC0) and minimal (CC1) residual disease (52.3 vs. 25.7), not reaching statistical significance. Ten patients are alive disease-free, and eight are alive with disease. CONCLUSIONS: Cytoreduction and HIPEC should not be excluded "a priori" for the treatment of peritoneal metastases from unconventional primary tumors. This combined therapeutic approach, performed in an experienced center, is safe and can provide a survival benefit over conventional palliative treatments