TY - JOUR

T1 - Extension of SEIR compartmental models for constructive Lyapunov control of COVID-19 and analysis in terms of practical stability

AU - Chen, Haiyue

AU - Haus, Benedikt

AU - Mercorelli, Paolo

N1 - This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Compartmental models

KW - COVID-19

KW - Lyapunov approach

KW - Practical stability

KW - Mathematics

KW - Engineering

UR - http://www.scopus.com/inward/record.url?scp=85114252690&partnerID=8YFLogxK

U2 - 10.3390/math9172076

DO - 10.3390/math9172076

M3 - Journal articles

AN - SCOPUS:85114252690

VL - 9

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 17

M1 - 2076

ER -