Open AccessOptimal vaccination strategies for an SEIR model of infectious diseases with logistic growth
Author(s) -
Markus Thäter,
Kurt Chudej,
Hans Josef Pesch
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.2018022
Subject(s) - optimal control , mathematical optimization , epidemic model , vaccination , logistic function , discretization , population , computer science , infectious disease (medical specialty) , control (management) , mathematics , control theory (sociology) , disease , medicine , artificial intelligence , machine learning , virology , mathematical analysis , environmental health , pathology
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.