Finite-time stability analysis and control of stochastic SIR epidemic model: A study of COVID-19

Nallappan Gunasekaran; R Vadivel; Guisheng Zhai; S Vinoth

doi:10.1016/j.bspc.2023.105123

Finite-time stability analysis and control of stochastic SIR epidemic model: A study of COVID-19

Biomed Signal Process Control. 2023 Sep:86:105123. doi: 10.1016/j.bspc.2023.105123. Epub 2023 Jun 13.

Authors

Nallappan Gunasekaran¹, R Vadivel², Guisheng Zhai³, S Vinoth⁴

Affiliations

¹ Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, China.
² Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket - 83000, Thailand.
³ Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan.
⁴ Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai - 600 069, Tamilnadu, India.

Abstract

Finite-time stability analysis is a powerful tool for understanding the long-term behavior of epidemiological models and has been widely used to study the spread of infectious diseases such as COVID-19. In this paper, we present a finite-time stability analysis of a stochastic susceptible-infected-recovered (SIR) epidemic compartmental model with switching signals. The model includes a linear parameter variation (LPV) and switching system that represents the impact of external factors, such as changes in public health policies or seasonal variations, on the transmission rate of the disease. We use the Lyapunov stability theory to examine the long-term behavior of the model and determine conditions under which the disease is likely to die out or persist in the population. By taking advantage of the average dwell time method and Lyapunov functional (LF) method, and using novel inequality techniques the finite-time stability (FTS) criterion in linear matrix inequalities (LMIs) is developed. The finite-time stability of the resultant closed-loop system, with interval and linear parameter variation (LPV), is then guaranteed by state feedback controllers. By analyzing the modified SIR model with these interventions, we are able to examine the efficiency of different control measures and determine the most appropriate response to the COVID-19 pandemic and demonstrate the efficacy of the suggested strategy through simulation results.

Keywords: Finite-time stability; Linear matrix inequalities; Lyapunov method; Stochastic disturbance; Switching signal.