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

Markus Thäter; Kurt Chudej; Hans Josef Pesch; Markus Thäter; Kurt Chudej; Hans Josef Pesch

doi:10.3934/mbe.2018022

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 2: 485-505. doi: 10.3934/mbe.2018022

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

Chair of Mathematics in Engineering Sciences, University of Bayreuth, Bayreuth, D 95440, Germany

Received: 30 July 2016 Accepted: 15 May 2017 Published: 01 April 2018
MSC : Primary: 49K15, 49M25, 90C90, 92D30; Secondary: 34A34

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.
- SEIR model,
- logistic growth,
- infectious diseases,
- optimal control,
- vaccination strategy,
- verification of numerical results
Citation: Markus Thäter, Kurt Chudej, Hans Josef Pesch. Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth[J]. Mathematical Biosciences and Engineering, 2018, 15(2): 485-505. doi: 10.3934/mbe.2018022

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Abstract

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.

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