An epidemic model with noisy parameters

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 co...

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Bibliographic Details
Published inMathematical biosciences Vol. 287; pp. 36 - 41
Main Author Roberts, M.G.
Format Journal Article
LanguageEnglish
Published United States Elsevier Inc 01.05.2017
Elsevier Science Ltd
Subjects
Amplitudes
Computer simulation
Epidemics
Epidemiology
Final size
Humans
Mathematical models
Models, Theoretical
Numerical analysis
Parameters
Perturbation methods
Simulation
SIR model
Size distribution
Standard deviation
Stochastic epidemic model
Stochastic Processes
Studies
Variations
Stochastic epidemic model
SIR model
Final size
Online AccessGet full text
ISSN0025-5564
1879-3134
DOI10.1016/j.mbs.2016.08.002

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Summary: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.
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ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2016.08.002