The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally)

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doi:10.3934/mbe.2018001

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2018, Volume 15, Issue 1: 1-20. Doi: 10.3934/mbe.2018001

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The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally)

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1.
ADAMSS, Universitá degli Studi di Milano, 20133 MILANO, Italy
2.
Faculty of Mathematics, "Alexandru Ioan Cuza" University of Iași, "Octav Mayer" Institute of Mathematics of the Romanian Academy, Iași 700506, Romania

* Corresponding author: Vincenzo Capasso
* Corresponding author: Vincenzo Capasso

Received: January 11, 2016

Accepted: October 29, 2016

Published: January 2018

The first author wishes to dedicate this review to the late Enea Grosso, Professor of Public Health and Hygiene in Bari, who had inspired most of the work presented here on man-environment epidemic systems

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Abstract

A review is presented here of the research carried out, by a group including the authors, on the mathematical analysis of epidemic systems. Particular attention is paid to recent analysis of optimal control problems related to spatially structured epidemics driven by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of harvesting type is related to the magnitude of the principal eigenvalue of a certain operator. The problem of finding the optimal position (by translation) of the support of the feedback stabilizing control is faced, in order to minimize both the infected population and the pollutant at a certain finite time.

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Mathematics Subject Classification: Primary: 35K57, 92D30, 93C20, 93D15; Secondary: 00-02, 92-02, 92-03.

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Figure 1. The transfer diagram for an SEIR compartmental model including the susceptible class S, the exposed, but not yet infective, class E, the infective class I, and the removed class R

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Figure 2. Nonlinear forces of infection [29]

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Figure 3. Think Globally, Act Locally

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