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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Published in | Mathematical biosciences Vol. 287; pp. 36 - 41 |
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Main Author | |
Format | Journal Article |
Language | English |
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United States
Elsevier Inc
01.05.2017
Elsevier Science Ltd |
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ISSN | 0025-5564 1879-3134 |
DOI | 10.1016/j.mbs.2016.08.002 |
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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. |
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AbstractList | 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. |
Author | Roberts, M.G. |
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Cites_doi | 10.1016/j.epidem.2014.05.002 10.1016/j.physa.2005.02.057 10.1098/rsif.2007.1031 10.1137/10081856X 10.1007/s00285-012-0611-0 10.1016/j.mbs.2009.10.001 10.1016/j.mbs.2010.01.006 10.1016/j.mbs.2015.05.004 10.1016/j.epidem.2014.09.006 10.1007/s00285-012-0540-y |
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Keywords | Stochastic epidemic model SIR model Final size |
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References | Roberts (bib0011) 2007; 4 Daley, Gani (bib0005) 1999 Gray, Greenhalgh, Hu, Mao, Pan (bib0009) 2011; 71 Duan (bib0007) 2015 Tornatore, Buccellato, Vetro (bib0014) 2005; 354 Ed-Darraz, Khaladi (bib0008) 2015; 266 Roberts (bib0012) 2013; 66 Diekmann, Heesterbeek, Britton (bib0006) 2013 Øksendal (bib0010) 1995 Roberts, Andreasen, Lloyd, Pellis (bib0013) 2015; 10 Bacaër, Khaladi (bib0001) 2013; 67 Britton (bib0002) 2010; 225 Britton, Lindenstrand (bib0003) 2009; 222 Britton, House, Lloyd, Mollison, Riley, Trapman (bib0004) 2015; 10 Bacaër (10.1016/j.mbs.2016.08.002_bib0001) 2013; 67 Britton (10.1016/j.mbs.2016.08.002_bib0002) 2010; 225 Roberts (10.1016/j.mbs.2016.08.002_bib0012) 2013; 66 Roberts (10.1016/j.mbs.2016.08.002_bib0011) 2007; 4 Roberts (10.1016/j.mbs.2016.08.002_bib0013) 2015; 10 Diekmann (10.1016/j.mbs.2016.08.002_bib0006) 2013 Britton (10.1016/j.mbs.2016.08.002_bib0003) 2009; 222 Tornatore (10.1016/j.mbs.2016.08.002_bib0014) 2005; 354 Duan (10.1016/j.mbs.2016.08.002_bib0007) 2015 Øksendal (10.1016/j.mbs.2016.08.002_bib0010) 1995 Daley (10.1016/j.mbs.2016.08.002_bib0005) 1999 Britton (10.1016/j.mbs.2016.08.002_bib0004) 2015; 10 Gray (10.1016/j.mbs.2016.08.002_bib0009) 2011; 71 Ed-Darraz (10.1016/j.mbs.2016.08.002_bib0008) 2015; 266 |
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SubjectTerms | 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 |
Title | An epidemic model with noisy parameters |
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