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Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

Title data

Thäter, Markus ; Chudej, Kurt ; Pesch, Hans Josef:
Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth.
In: Mathematical Biosciences and Engineering. Vol. 15 (April 2018) Issue 2 . - pp. 485-505.
ISSN 1551-0018
DOI: https://doi.org/10.3934/mbe.2018022

Official URL: Volltext

Abstract in another language

In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: SEIR model; logistic growth; infectious diseases; optimal control; vaccination strategy; verification of numerical results
Subject classification: 49K15, 49M25, 90C90, 92D30, 34A34
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors > Chair Mathematics in Engineering Sciences - Univ.-Prof. Dr. Hans-Josef Pesch
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen > CLehrstuhl Wissenschaftliches Rechnen - Univ.-Prof. Dr. Mario Bebendorf
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
600 Technology, medicine, applied sciences > 610 Medicine and health
Date Deposited: 19 Jun 2017 08:26
Last Modified: 20 Sep 2018 08:41
URI: https://eref.uni-bayreuth.de/id/eprint/37967