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Infectious Disease Modelling 2018年第1期3卷 1-12页

作者： Mauricio Santillana Ashleigh Tuite Tahmina Nasserie Paul Fine David Champredon leonid chindelevitch Jonathan Dushoff David Fisman Computation Health Informatics Program Boston Children's HospitalBostonMAUSA Department of Pediatrics Harvard Medical SchoolBontonMAUSA Dalla Lana School of Public Health University of TorontoTorontoOntarioCanada BlueDot TorontoOntarioCanada Department of Infectious Disease Epidemiology London School of Hygiene and Tropical MedicineLondonUK Agent-Based Modelling Laboratory York UniversityTorontoOntarioCanada School of Computing Science Simon Fraser UniversityBurnabyBritish ColumbiaCanada Department of Theoretical Biology McMaster UniversityHamiltonOntarioCanada Department of Medicine Faculty of MedicineUniversity of TorontoTorontoOntarioCanada

Mathematical models are often regarded as recent innovations in the description and analysis of infectious disease outbreaks and epidemics,but simple mathematical expressions have been in use for projection of epidemic trajectories for more than a *** recently introduced a single equation model(the incidence decay with exponential adjustment,or IDEA model)that can be used for short-term epidemiological *** the mid-19th century,*** Farr made the observation that epidemic events rise and fall in a roughly symmetrical pattern that can be approximated by a bell-shaped *** noticed that this time-evolution behavior could be captured by a single mathematical formula(“Farr's law”)that could be used for epidemic *** show here that the IDEA model follows Farr's law,and show that for intuitive assumptions,Farr's Law can be derived from the IDEA ***,we show that both mathematical approaches,Farr's Law and the IDEA model,resemble solutions of a susceptible-infectious-removed(SIR)compartmental differential-equation model in an asymptotic limit,where the changes of disease transmission respond to control measures,and not only to the depletion of susceptible *** suggests that the concept of the reproduction number eR 0T was implicitly captured in Farr's(pre-microbial era)work,and also suggests that control of epidemics,whether via behavior change or intervention,is as integral to the natural history of epidemics as is the dynamics of disease transmission.

关键词： equation exponential decay

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