A vector valued optimization approach to the study of a class of epidemics
type: Item
instance of: scholarly article
title: A vector valued optimization approach to the study of a class of epidemics
zbMATH Open document ID: 0727.92024
DOI: 10.1016/0022-247X(91)90014-Q
author: N. Basile
author: Michele Mininni
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors present a polyoptimization problem for a reaction-diffusion system which models the spread of an epidemic of oro-fecal origin. A solution of the system is unique for all control functions representing a sanitation program in the city placed on the coast of the sea and on the coast itself. The specific initial and boundary conditions have a mixed character. The uncontrolled system is described by a linear parabolic model while the control part is given by bilinear continuous operators. The objectives for the optimization represent the cost of the sanitation activities, the cost of the epidemic itself and the economic (psychological) effects of the duration of the epidemic. The authors discuss an existence result for Pareto optimal solutions and give necessary conditions for solutions which follow from the generalized Pontryagin maximum principle.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 4202096
zbMATH Keywords: multiobjective optimization
zbMATH Keywords: abstract maximum principle
zbMATH Keywords: spread of epidemics
zbMATH Keywords: mixed initial-boundary conditions
zbMATH Keywords: polyoptimization problem
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: epidemic of oro-fecal origin
zbMATH Keywords: sanitation program
zbMATH Keywords: linear parabolic model
zbMATH Keywords: bilinear continuous operators
zbMATH Keywords: existence result for Pareto optimal solutions
zbMATH Keywords: generalized Pontryagin maximum principle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4202096