title: An epidemic model with noisy parameters.
abstract: We analyse an SIR model where the epidemiological parameters are subject to small amplitude random fluctuations. We derive a final size equation and extend the result to an SEIR model. We use a small amplitude perturbation to estimate the expected final size of the SIR model and its variance, and compare the result with numerical simulations. We show that although individual realisations may exhibit considerable variation around solutions of the deterministic model, the mean of the final size distribution is in good agreement with the deterministic final size, and its standard deviation is small compared to the mean.
authors: Infectious Disease Research Centre, Institute of Natural & Mathematical Sciences and New Zealand Institute for Advanced Study, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand. Electronic address: m.g.roberts@massey.ac.nz.
authors: M G
authors: MG
authors: Roberts
mesh_terms: D058872:Epidemics; D006801:Humans; D008962:Models, Theoretical; D013269:Stochastic Processes
keywords: Final size; SIR model; Stochastic epidemic model