The dynamics of entropy in the COVID-19 outbreaks
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ORIGINAL PAPER
The dynamics of entropy in the COVID-19 outbreaks Ziqi Wang · Marco Broccardo · Arnaud Mignan · Didier Sornette
Received: 10 July 2020 / Accepted: 31 July 2020 © The Author(s) 2020
Abstract With the unfolding of the COVID-19 pandemic, mathematical modelling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long-term predictions were extremely challenging to address. In addiThis research received no specific Grant from any funding agency in the public, commercial, or not-for-profit sectors. Z. Wang (B) Earthquake Engineering Research and Test Center, Guangzhou University, Guangzhou, China e-mail: [email protected] M. Broccardo (B) Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy e-mail: [email protected] M. Broccardo Institute for Risk and Uncertainties, University of Liverpool, Liverpool, UK A. Mignan · D. Sornette Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, China e-mail: [email protected] A. Mignan Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, China D. Sornette Chair of Entrepreneurial Risks, Department of Management, Technology, and Economics, ETH Zürich, Zurich, Switzerland e-mail: [email protected]
tion, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modelling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed for describing the evolution of entropy during the COVID-19 pandemic together with the instantaneous reproductive ratio. Then, we introduce and use entropy-based metrics of global transmission to measure the impact and the temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modelled by an equation governing the probability distribution that describes a nonlinear Markov process of a statistically averaged individual, leading to a clear physical interpretation. The time-dependent parameters are formulated by adaptive basis functions, leading to a parsimonious representation. In addition, we provide a full Bayesian inversion scheme for calibration together with a coherent strategy to address data unreliability. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the susceptible–exposed–infected–removed model. Applying the model to the Hubei region, South
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