Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk
Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk
Abstract The damage of the novel Coronavirus disease (COVID-19) is reaching unprecedented scales. There are numerous classical epidemiology models trying to quantify epidemiology metrics. Usually, to forecast epidemics, classical approaches need parameter estimations, such as the contagion rate or the basic reproduction number. Here, we propose a data-driven, parameter-free, geometric approach to access the emergence of a pandemic state by studying the Forman-Ricci and Ollivier-Ricci network curvatures. Discrete Ollivier-Ricci curvature has been used successfully to forecast risk in financial networks and we suggest that those results can provide analogous results for COVID-19 epidemic time-series. We first compute both curvatures in a toy-model of epidemic time-series with delays, which allows us to create epidemic networks. By doing so, we are able to verify that the Ollivier-Ricci and Forman-Ricci curvatures can be a parameter-free estimate for identifying a pandemic state in the simulated epidemic. On this basis, we then compute both Forman-Ricci and Ollivier-Ricci curvatures for real epidemic networks built from COVID-19 epidemic time-series available at the World Health Organization (WHO). Both curvatures allow us to detect early warning signs of the emergence of the pandemic. The advantage of our method lies in providing an early geometrical data marker for the pandemic state, regardless of parameter estimation and stochastic modelling. This work opens the possibility of using discrete geometry to study epidemic networks.
da Silva Hernande P.、dos Santos Everlon Figueir?a、de Lima Filho Jos¨| Luiz、Santos Fernando A. N.、de Souza Danillo Barros、Correia Jailson B.、da Cunha Jonatas T. S.、Albuquerque Jones
Instituto para Redu??o de Riscos e Desastres de Pernambuco - Universidade Federal Rural de Pernambuco (IRRD-PE) and Laborat¨?rio de Imunopatologia Keizo Asami (LIKA) - Universidade de Federal de Pernambuco (UFPE)Departamento de Matem¨￠tica, Universidade Federal de Pernambuco (UFPE)Instituto para Redu??o de Riscos e Desastres de Pernambuco - Universidade Federal Rural de Pernambuco (IRRD-PE) and Laborat¨?rio de Imunopatologia Keizo Asami (LIKA) - Universidade de Federal de Pernambuco (UFPE)Departamento de Matem¨￠tica, Universidade Federal de Pernambuco (UFPE) Department of Anatomy & Neurosciences, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam NeuroscienceDepartamento de Matem¨￠tica, Universidade Federal de Pernambuco (UFPE)Instituto para Redu??o de Riscos e Desastres de Pernambuco - Universidade Federal Rural de Pernambuco (IRRD-PE) and Laborat¨?rio de Imunopatologia Keizo Asami (LIKA) - Universidade de Federal de Pernambuco (UFPE)Departamento de Matem¨￠tica, Universidade Federal de Pernambuco (UFPE)Instituto para Redu??o de Riscos e Desastres de Pernambuco - Universidade Federal Rural de Pernambuco (IRRD-PE) and Laborat¨?rio de Imunopatologia Keizo Asami (LIKA) - Universidade de Federal de Pernambuco (UFPE)
医学研究方法基础医学数学
COVID-19SARS2Forman-Ricci CurvatureOllivier-Ricci curvatureEpidemiologyTopological Data Analysis
da Silva Hernande P.,dos Santos Everlon Figueir?a,de Lima Filho Jos¨| Luiz,Santos Fernando A. N.,de Souza Danillo Barros,Correia Jailson B.,da Cunha Jonatas T. S.,Albuquerque Jones.Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk[EB/OL].(2025-03-28)[2025-04-24].https://www.medrxiv.org/content/10.1101/2020.04.01.20047225.点此复制
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