A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed indi...

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Bibliographic Details
Published inMathematics of control, signals, and systems Vol. 36; no. 2; pp. 297 - 327
Main Authors Chyba, Monique, Klotz, Taylor, Mileyko, Yuriy, Shanbrom, Corey
Format Journal Article
LanguageEnglish
Published London Springer London 01.06.2024
Springer Nature B.V
Subjects
Communications Engineering
Control
Epidemiology
Immunization
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Optimal control
Original Article
Papers dedicated to Eduardo D. Sontag on the occasion of his 70th birthday
Robotics
Systems Theory
Compartmental model
Endemic threshold
Static feedback linearization
Optimal control
Endemic equilibrium
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Summary:Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. In the first part of this paper, we propose two new compartmental epidemiological models and study their equilibria, obtaining an endemic threshold theorem for the first model. In the second part of the paper, we treat the second model as an affine control system with two controls: vaccination and mitigation. We show that this system is static feedback linearizable, presents some simulations, and investigates an optimal control version of the problem. We conclude with some open problems and ideas for future research.
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-023-00365-2