Predicting Unobserved Exposures from Seasonal Epidemic Data

Eric Forgoston, Ira B. Schwartz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very long times.

Original languageEnglish
Pages (from-to)1450-1471
Number of pages22
JournalBulletin of Mathematical Biology
Issue number9
StatePublished - Sep 2013


  • Epidemics with seasonality and noise
  • Model reduction


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