Open AccessThe interplay between models and public health policies: Regional control for a class of spatially structured epidemics <em>(think globally, act locally)</em>
Author(s) -
Vincenzo Capasso,
Sebastian Aniţa
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2018001
Subject(s) - control (management) , domain (mathematical analysis) , principal (computer security) , population , optimal control , operator (biology) , class (philosophy) , mathematics , control theory (sociology) , computer science , mathematical optimization , sociology , demography , biology , mathematical analysis , biochemistry , repressor , artificial intelligence , transcription factor , gene , operating system
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.