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 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
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ISSN0025-5564
1879-3134
DOI10.1016/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.
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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  email: m.g.roberts@massey.ac.nz
  organization: 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
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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
Language English
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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
References_xml – volume: 222
  start-page: 109
  year: 2009
  end-page: 116
  ident: bib0003
  article-title: Epidemic modelling: aspects where stochasticity matters
  publication-title: Math. Biosci.
– volume: 71
  start-page: 876
  year: 2011
  end-page: 902
  ident: bib0009
  article-title: A stochastic differential equation SIS epidemic model
  publication-title: SIAM J. Appl. Math.
– year: 2013
  ident: bib0006
  publication-title: Mathematical Tools for Understanding Infectious Disease Dynamics
– volume: 66
  start-page: 1463
  year: 2013
  end-page: 1474
  ident: bib0012
  article-title: Epidemic models with uncertainty in the reproduction number
  publication-title: J. Math. Biol.
– year: 2015
  ident: bib0007
  publication-title: An Introduction to Stochastic Dynamics
– volume: 10
  start-page: 54
  year: 2015
  end-page: 57
  ident: bib0004
  article-title: Five challenges for stochastic epidemic models involving global transmission
  publication-title: Epidemics
– volume: 4
  start-page: 949
  year: 2007
  end-page: 961
  ident: bib0011
  article-title: The pluses and minuses of
  publication-title: J. R. Soc. Interface
– volume: 67
  start-page: 1729
  year: 2013
  end-page: 1739
  ident: bib0001
  article-title: On the basic reproduction number in a random environment
  publication-title: J. Math. Biol.
– volume: 225
  start-page: 24
  year: 2010
  end-page: 35
  ident: bib0002
  article-title: Stochastic epidemic models: a survey
  publication-title: Math. Biosci.
– volume: 266
  start-page: 10
  year: 2015
  end-page: 14
  ident: bib0008
  article-title: On the final size of epidemics in random environment
  publication-title: Math. Biosci.
– volume: 10
  start-page: 49
  year: 2015
  end-page: 53
  ident: bib0013
  article-title: Nine challenges for deterministic epidemic models
  publication-title: Epidemics
– year: 1999
  ident: bib0005
  publication-title: Epidemic Modelling: An Introduction
– volume: 354
  start-page: 111
  year: 2005
  end-page: 126
  ident: bib0014
  article-title: Stability of a stochastic SIR system
  publication-title: Physica A
– year: 1995
  ident: bib0010
  publication-title: Stochastic Differential Equations
– year: 1995
  ident: 10.1016/j.mbs.2016.08.002_bib0010
– volume: 10
  start-page: 54
  year: 2015
  ident: 10.1016/j.mbs.2016.08.002_bib0004
  article-title: Five challenges for stochastic epidemic models involving global transmission
  publication-title: Epidemics
  doi: 10.1016/j.epidem.2014.05.002
– year: 1999
  ident: 10.1016/j.mbs.2016.08.002_bib0005
– volume: 354
  start-page: 111
  year: 2005
  ident: 10.1016/j.mbs.2016.08.002_bib0014
  article-title: Stability of a stochastic SIR system
  publication-title: Physica A
  doi: 10.1016/j.physa.2005.02.057
– year: 2013
  ident: 10.1016/j.mbs.2016.08.002_bib0006
– volume: 4
  start-page: 949
  year: 2007
  ident: 10.1016/j.mbs.2016.08.002_bib0011
  article-title: The pluses and minuses of R0
  publication-title: J. R. Soc. Interface
  doi: 10.1098/rsif.2007.1031
– volume: 71
  start-page: 876
  year: 2011
  ident: 10.1016/j.mbs.2016.08.002_bib0009
  article-title: A stochastic differential equation SIS epidemic model
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/10081856X
– volume: 67
  start-page: 1729
  year: 2013
  ident: 10.1016/j.mbs.2016.08.002_bib0001
  article-title: On the basic reproduction number in a random environment
  publication-title: J. Math. Biol.
  doi: 10.1007/s00285-012-0611-0
– volume: 222
  start-page: 109
  year: 2009
  ident: 10.1016/j.mbs.2016.08.002_bib0003
  article-title: Epidemic modelling: aspects where stochasticity matters
  publication-title: Math. Biosci.
  doi: 10.1016/j.mbs.2009.10.001
– volume: 225
  start-page: 24
  year: 2010
  ident: 10.1016/j.mbs.2016.08.002_bib0002
  article-title: Stochastic epidemic models: a survey
  publication-title: Math. Biosci.
  doi: 10.1016/j.mbs.2010.01.006
– volume: 266
  start-page: 10
  year: 2015
  ident: 10.1016/j.mbs.2016.08.002_bib0008
  article-title: On the final size of epidemics in random environment
  publication-title: Math. Biosci.
  doi: 10.1016/j.mbs.2015.05.004
– volume: 10
  start-page: 49
  year: 2015
  ident: 10.1016/j.mbs.2016.08.002_bib0013
  article-title: Nine challenges for deterministic epidemic models
  publication-title: Epidemics
  doi: 10.1016/j.epidem.2014.09.006
– volume: 66
  start-page: 1463
  year: 2013
  ident: 10.1016/j.mbs.2016.08.002_bib0012
  article-title: Epidemic models with uncertainty in the reproduction number
  publication-title: J. Math. Biol.
  doi: 10.1007/s00285-012-0540-y
– year: 2015
  ident: 10.1016/j.mbs.2016.08.002_bib0007
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Snippet 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...
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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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