The dynamics of entropy in the COVID-19 outbreaks.

Ziqi Wang, Marco Broccardo, Arnaud Mignan, Didier Sornette
Author Information
  1. Ziqi Wang: Earthquake Engineering Research and Test Center, Guangzhou University, Guangzhou, China. ORCID
  2. Marco Broccardo: Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, Italy. ORCID
  3. Arnaud Mignan: Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, China. ORCID
  4. Didier Sornette: Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, China. ORCID

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 addition, 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 Korean, Italian, Spanish, German, and French COVID-19 datasets, we discover significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio.

Keywords

References

  1. Lancet Public Health. 2020 May;5(5):e261-e270 [PMID: 32220655]
  2. Cell Discov. 2020 Feb 24;6:10 [PMID: 32133152]
  3. J Thorac Dis. 2020 Mar;12(3):165-174 [PMID: 32274081]
  4. Lancet Infect Dis. 2020 May;20(5):559-564 [PMID: 32220284]
  5. J Biol Dyn. 2012;6:509-23 [PMID: 22873603]
  6. Lancet. 2020 Apr 25;395(10233):1382-1393 [PMID: 32277878]
  7. BMJ Open. 2021 Jan 4;11(1):e043577 [PMID: 33397669]
  8. Lancet Infect Dis. 2020 Jun;20(6):669-677 [PMID: 32240634]
  9. Lancet. 2020 Feb 29;395(10225):689-697 [PMID: 32014114]
  10. Lancet Infect Dis. 2020 Jun;20(6):689-696 [PMID: 32220650]
  11. Nat Commun. 2019 Feb 22;10(1):898 [PMID: 30796206]
  12. Lancet. 2020 Mar 28;395(10229):1047-1053 [PMID: 32199075]
  13. JAMA. 2020 Mar 17;323(11):1061-1069 [PMID: 32031570]
  14. J Theor Biol. 2004 Jul 7;229(1):119-26 [PMID: 15178190]
  15. Lancet. 2020 Apr 4;395(10230):1137-1144 [PMID: 32178768]
  16. Korean J Intern Med. 2018 Mar;33(2):233-246 [PMID: 29506344]
  17. Theor Popul Biol. 2011 Dec;80(4):256-64 [PMID: 22019889]
  18. IEEE Trans Netw Sci Eng. 2020 Sep 18;7(4):3279-3294 [PMID: 37981959]
  19. Lancet. 2020 Feb 15;395(10223):497-506 [PMID: 31986264]
  20. Proc Natl Acad Sci U S A. 2020 May 12;117(19):10484-10491 [PMID: 32327608]
  21. Ann Intern Med. 2020 May 05;172(9):577-582 [PMID: 32150748]
  22. Philos Trans R Soc Lond B Biol Sci. 2021 Jul 19;376(1829):20200265 [PMID: 34053269]
  23. Nonlinear Dyn. 2020;101(3):1561-1581 [PMID: 32836822]
  24. Biometrics. 2006 Dec;62(4):1170-7 [PMID: 17156292]
  25. Euro Surveill. 2020 Jan;25(4): [PMID: 32019667]

Word Cloud

Created with Highcharts 10.0.0evolutionentropyCOVID-19pandemicmodelframeworkinstantaneousreproductiveratioprocessmodellingusedunderstandinggoverningeventclearaddressadditionmetricglobaloutbreaksdynamicstransmissiontogethertemporalMarkovleadingBayesianabsolutechangeunfoldingmathematicalepidemicsperceivedcentralelementpredictingHoweversoonbecamelong-termpredictionsextremelychallengingstillunclearshalldescriptionYetrobustconsistentchoicecrucialin-depthmacroscopicphenomenologybetter-informedmitigationstrategiesstudyproposeMarkovianstochasticdesigneddescribingintroduceuseentropy-basedmetricsmeasureimpactformulationoutbreakmodelledequationprobabilitydistributiondescribesnonlinearstatisticallyaveragedindividualphysicalinterpretationtime-dependentparametersformulatedadaptivebasisfunctionsparsimoniousrepresentationprovidefullinversionschemecalibrationcoherentstrategydataunreliabilitytimeratesystemnaturaltransparentoutputsappealingpropertyapplicablecompartmentalepidemicillustrationapplyproposedapproachsimplemodificationsusceptible-exposed-infected-removedApplyingHubeiregionSouthKoreanItalianSpanishGermanFrenchdatasetsdiscoversignificantdifferencehighlyregulartrendsanalysisNonlinearStochasticUncertaintyquantification

Similar Articles

Cited By