title: Predicting unobserved exposures from seasonal epidemic data.
abstract: 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.
authors.affiliation: Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043, USA. eric.forgoston@montclair.edu
authors.forename: Eric
authors.initials: E
authors.lastname: Forgoston
authors.forename: Ira B
authors.initials: IB
authors.lastname: Schwartz
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology; D019295:Computational Biology; D058872:Epidemics / Q000706:statistics & numerical data*; D015981:Epidemiologic Factors; D006801:Humans; D008457:Measles / Q000453:epidemiology; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D012621:Seasons; D013269:Stochastic Processes; D006113:United Kingdom / Q000453:epidemiology