As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r ( t ) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r ( t ) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document} β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta > \beta _c$$\end{document} β > β c ) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta < \beta _c$$\end{document} β < β c ) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r(t) \approx 1$$\end{document} r ( t ) ≈ 1 hovering around its threshold value.
【저자키워드】 Applied mathematics, Statistics, Nonlinear phenomena, Phase transitions and critical phenomena, Computer modelling, 【초록키워드】 COVID-19, public health, Evolution, lockdown, COVID-19 pandemic, Infection, Epidemics, Epidemic, Research, Community, epidemiological, threshold, disease, Critical, disease transmission, Analysis, growth, complex, measure, threshold value, the epidemic, fluctuation, Course, evaluate, significantly, applied, treated, imperative, explain, mathematical, progressed, 【제목키워드】 COVID-19, Epidemic, fluctuation, explain,