Epidemiological Control of COVID-19 Through the Theory of Variable Structure and Sliding Mode Systems

Abstract

This paper proposes a new mathematical model called SIRDQ considering control laws for the government actions in order to reduce the quarantine periods. The proposed control laws guarantee the regulation of the effective number of reproduction to a desired value, which is directly related to the propagation of the epidemic model. We consider two control strategies based on first-order sliding mode and super-twisting algorithm due to its robustness with respect to parametric uncertainties and disturbances, as found in epidemiological models. The stability analysis of the closed-loop system is rigorously presented. Simulations show that the employed control strategies assure better levels of isolation to be adopted.

A Multi-Agent-Based Simulation Model for the Spreading of Diseases Through Social Interactions During Pandemics

“…The automation and control community in Brazil is also concerned with the pandemic situation, counting with contributions of many researchers in the modeling and control of epidemics. Santos et al ( 2022 ) present an equation-based model within a sliding modes control strategy. The work of Batista et al.…”

HBV Epidemic Control Using Time-Varying Sliding Mode Control Method

“…With these compartment models, control policies including measures such as vaccination, and treatment and isolation controls can be drawn by using dynamic optimization approach according to Pontryagin's maximum principle [10][11][12][13][14][15][16][17] . Another potential approach is to use feedback control approach to set the policy [18][19][20][21][22][23][24][25][26][27][28][29][30] . Feedback control could deal with the uncertainties and disturbances which occur in the system.…”

“…Moreover, it is an efficient approach to set the policy in an analytical form 31 . Applying feedback control to define the measures of the control policy showed the feasibility and the efficiency in the previous studies of this approach [18][19][20][21][22][23][24][25][26][27][28][29][30] . Sliding mode control (SMC) is a robust feedback control which has been employed to control various nonlinear dynamical systems [32][33][34] .…”

“…Sliding mode control (SMC) is a robust feedback control which has been employed to control various nonlinear dynamical systems [32][33][34] . Moreover, the SMC method has been applied to synthesize the control policy for the biological systems such as ecosystems and epidemic models 18,24,[27][28][29][30][35][36] . For the epidemic systems, the sliding mode control was applied to set the control policy of the epidemic systems in the form of a compartment model 18,24,[27][28][29][30] .…”

“…Moreover, the SMC method has been applied to synthesize the control policy for the biological systems such as ecosystems and epidemic models 18,24,[27][28][29][30][35][36] . For the epidemic systems, the sliding mode control was applied to set the control policy of the epidemic systems in the form of a compartment model 18,24,[27][28][29][30] . The SMC with an integral sliding surface can eliminate the steady state errors of the control systems as applied to control various engineering systems 37,40,41 .…”