Fuzzy Sliding Mode Controller Design and Analysis of an SQEIAR Epidemic Model for COVID-19 to Determine the Quarantine Rate

Abstract

According to the global prevalence of coronavirus (COVID-19) pandemic, mathematical models can predict and control the dynamic behavior of the pandemic. Therefore, in this study, a comprehensive model is considered to examine the trend of COVID-19 based on Susceptible, Exposed, Infected (Symptomatic and Asymptomatic), and Recovered individuals. In the absence of a curative treatment or vaccination campaign, the group of "quarantined people" is added to the model. Then, a positivity analysis of states is examined, and the threshold criterion (𝑅 0 ) is determined. The equilibrium points (disease-free and endemic) are also calculated, and their stability is investigated using the Jacobin matrix. The quarantine rate is regulated as the only control input using the fuzzy sliding mode controller. The efficiency of the controller is also investigated in the presence of uncertainty in model parameters. Also, the impact of the infected community on other communities, considering the controller, will be examined. Finally, the performance and efficiency of the proposed controller are evaluated.