Optimal intervention strategies for a SEIR control model of ebola epidemics
type: Item
instance of: scholarly article
title: Optimal intervention strategies for a SEIR control model of ebola epidemics
zbMATH Open document ID: 1330.49039
author: Ellina V. Grigorieva
author: E. N. Khailov
published in: Mathematics
publication date: 2016-01-12T00:00:00Z
review text: Summary: A SEIR control model describing the ebola epidemic in a population of a constant size is considered over a given time interval. It contains two intervention control functions reflecting efforts to protect susceptible individuals from infected and exposed individuals. For this model, the problem of minimizing the weighted sum of total fractions of infected and exposed individuals and total costs of intervention control constraints at a given time interval is stated. For the analysis of the corresponding optimal controls, the Pontryagin maximum principle is used. According to it, these controls are bang-bang, and are determined using the same switching function. A linear non-autonomous system of differential equations, which this function satisfies together with its corresponding auxiliary functions, is found. In order to estimate the number of zeros of the switching function, the matrix of the linear non-autonomous system is transformed to an upper triangular form on the entire time interval and the generalized Rolle's theorem is applied to the converted system of differential equations. It is found that the optimal controls of the original problem have at most two switchings. This fact allows the reduction of the original complex optimal control problem to the solution of a much simpler problem of conditional minimization of a function of two variables. Results of the numerical solution to this problem and their detailed analysis are provided.
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49K30
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 6528857
zbMATH Keywords: SEIR model
zbMATH Keywords: ebola epidemic
zbMATH Keywords: nonlinear control system
zbMATH Keywords: optimal intervention strategies
zbMATH Keywords: Pontryagin maximum principle
zbMATH Keywords: bang-bang controls
zbMATH Keywords: non-autonomous quadratic differential system
zbMATH Keywords: generalized Rolle's theorem
MaRDI profile type: Publication
full work available at URL: math3040961
OpenAlex ID: W1808709171
Wikidata QID: Q113174916
cites work: Optimal control of deterministic epidemics
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DOI: 10.3390/MATH3040961
description: scientific article; zbMATH DE number 6528857