Extension of SEIR compartmental models for constructive Lyapunov control of COVID-19 and analysis in terms of practical stability

Research output: Journal contributionsJournal articlesResearchpeer-review

Authors

Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of different considered populations as Susceptible, Exposed, Infected and Recovered compartments (SEIR). This study derives control-oriented compartmental models of the pandemic, together with constructive control laws based on the Lyapunov theory. The paper presents the derivation of new vaccination and quarantining strategies, found using compartmental models and design methods from the field of Lyapunov theory. The Lyapunov theory offers the possibility to track desired trajectories, guaran-teeing the stability of the controlled system. Computer simulations aid to demonstrate the efficacy of the results. Stabilizing control laws are obtained and analyzed for multiple variants of the model. The stability, constructivity, and feasibility are proven for each Lyapunov-like function. Obtaining the proof of practical stability for the controlled system, several interesting system properties such as herd immunity are shown. On the basis of a generalized SEIR model and an extended variant with additional Protected and Quarantined compartments, control strategies are conceived by using two fundamental system inputs, vaccination and quarantine, whose influence on the system is a crucial part of the model. Simulation results prove that Lyapunov-based approaches yield effective control of the disease transmission.

Original languageEnglish
Article number2076
JournalMathematics
Volume9
Issue number17
Number of pages25
DOIs
Publication statusPublished - 09.2021

Bibliographical note

This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry

Documents

DOI

Recently viewed

Publications

  1. Combining Model Predictive and Adaptive Control for an Atomic Force Microscope Piezo-Scanner-Cantilever System
  2. A Control of an Electromagnetic Actuator Using Model Predictive Control
  3. Investigating quality raters' performance using interface evaluation methods
  4. Effects of plyometric training on postural control in static and dynamic testing situations
  5. Distributable Modular Software Framework for Manufacturing Systems
  6. Emancipative Values and Non-violent Protest
  7. Public Value: rethinking value creation
  8. Enacting migration through data practices
  9. Learning from Erroneous Examples
  10. Within-individual leaf trait variation increases with phenotypic integration in a subtropical tree diversity experiment
  11. Principals between exploitation and exploration
  12. Leaf trait variation within individuals mediates the relationship between tree species richness and productivity
  13. Embarrassment as a public vs. private emotion and symbolic coping behaviour
  14. Glancing into the Applied Tool Box
  15. Conceptions of problem solving mathematics teaching
  16. Modernizing persistence–bioaccumulation–toxicity (PBT) assessment with high throughput animal-free methods
  17. Different facets of tree sapling diversity influence browsing intensity by deer dependent on spatial scale
  18. The representative turn in EU studies
  19. Effects Of Different Order Processing Strategies On Operating Curves Of Logistic Models
  20. A Comparative Study for Fisheye Image Classification
  21. An intersection test for the cointegrating rank in dependent panel data
  22. Improvements and future challenges for the research infrastructure in the field firm level data
  23. Investigation of compression behavior of Mg-4Zn-2(Nd, Gd)-0.5Zr at 350°C by in situ synchrotron radiation diffraction
  24. Industry 4.0 more than a challenge in modeling, identification, and control for cyber-physical systems
  25. Temporal and thermodynamic irreversibility in production theory
  26. Riding Two Horses at The Same Time: Paradox Responses for Navigating Exploration and Exploitation in Small and Medium-Sized IT Consulting Firms
  27. Vimentin promoter methylation analysis is a suitable complement of a gene mutation marker panel for the detection of preneoplastic and neoplastic colonic lesions
  28. The frame of the game