Bull Math Biol (2019) 81:4343–4365 https://doi.org/10.1007/s11538-017-0284-3 SPECIAL ISSUE: MATHEMATICAL EPIDEMIOLOGY Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model Alexandra Smirnova 1 · Linda deCamp 1 · Gerardo Chowell 2 Received: 7 February 2017 / Accepted: 12 April 2017 / Published online: 2 May 2017 © Society for Mathematical Biology 2017 Abstract Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous stud- ies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polyno- mials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov’s) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabiliz- ing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014–2015 Ebola epidemic in West Africa. B Alexandra Smirnova asmirnova@gsu.edu Linda deCamp ldecamp1@student.gsu.edu Gerardo Chowell gchowell@gsu.edu 1 Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA 2 School of Public Health, Georgia State University, Atlanta, GA, USA 123