title: Using Phenomenological Models to Characterize Transmissibility and Forecast Patterns and Final Burden of Zika Epidemics.
abstract: BACKGROUND
  The World Health Organization declared the ongoing Zika virus (ZIKV) epidemic in the Americas a Public Health Emergency of International Concern on February 1, 2016. ZIKV disease in humans is characterized by a "dengue-like" syndrome including febrile illness and rash. However, ZIKV infection in early pregnancy has been associated with severe birth defects, including microcephaly and other developmental issues. Mechanistic models of disease transmission can be used to forecast trajectories and likely disease burden but are currently hampered by substantial uncertainty on the epidemiology of the disease (e.g., the role of asymptomatic transmission, generation interval, incubation period, and key drivers). When insight is limited, phenomenological models provide a starting point for estimation of key transmission parameters, such as the reproduction number, and forecasts of epidemic impact.
  
  
  METHODS
  We obtained daily counts of suspected Zika cases by date of symptoms onset from the Secretary of Health of Antioquia, Colombia during January-April 2016. We calibrated the generalized Richards model, a phenomenological model that accommodates a variety of early exponential and sub-exponential growth kinetics, against the early epidemic trajectory and generated predictions of epidemic size. The reproduction number was estimated by applying the renewal equation to incident cases simulated from the fitted generalized-growth model and assuming gamma or exponentially-distributed generation intervals derived from the literature. We estimated the reproduction number for an increasing duration of the epidemic growth phase.
  
  
  RESULTS
  The reproduction number rapidly declined from 10.3 (95% CI: 8.3, 12.4) in the first disease generation to 2.2 (95% CI: 1.9, 2.8) in the second disease generation, assuming a gamma-distributed generation interval with the mean of 14 days and standard deviation of 2 days. The generalized-Richards model outperformed the logistic growth model and provided forecasts within 22% of the actual epidemic size based on an assessment 30 days into the epidemic, with the epidemic peaking on day 36.
  
  
  CONCLUSIONS
  Phenomenological models represent promising tools to generate early forecasts of epidemic impact particularly in the context of substantial uncertainty in epidemiological parameters. Our findings underscore the need to treat the reproduction number as a dynamic quantity even during the early growth phase, and emphasize the sensitivity of reproduction number estimates to assumptions on the generation interval distribution.
authors.affiliation: Division of Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, Maryland, USA; Mathematical, Computational & Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, Arizona, USA.
authors.forename: Gerardo
authors.initials: G
authors.lastname: Chowell
authors.forename: Doracelly
authors.initials: D
authors.lastname: Hincapie-Palacio
authors.affiliation: Logic and Computation Group, EAFIT University, Medellin, Antioquia, Colombia.
authors.forename: Juan
authors.initials: J
authors.lastname: Ospina
authors.forename: Bruce
authors.initials: B
authors.lastname: Pell
authors.affiliation: School of Public Health, Georgia State University, Atlanta, Georgia, USA.
authors.forename: Amna
authors.initials: A
authors.lastname: Tariq
authors.affiliation: School of Public Health, Georgia State University, Atlanta, Georgia, USA.
authors.forename: Sushma
authors.initials: S
authors.lastname: Dahal
authors.affiliation: Agent Based Modelling Laboratory, York University, Toronto, Canada.
authors.forename: Seyed
authors.initials: S
authors.lastname: Moghadas
authors.affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, USA.
authors.forename: Alexandra
authors.initials: A
authors.lastname: Smirnova
authors.affiliation: Department of Public Health, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Lone
authors.initials: L
authors.lastname: Simonsen
authors.affiliation: Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, Maryland, USA.
authors.forename: Cécile
authors.initials: C
authors.lastname: Viboud