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Application I: Spread of Influenza

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Abstract

As a first application of the methods introduced in the first two parts of this book, this chapter investigates the spread of human influenza. More precisely, it analyses a well-known dataset on an influenza outbreak in a British boarding school and the spatial spread of influenza in Germany during the season 2009/10, in which the swine flu virus was prevalent. In the latter example, spatial mixing of individuals is estimated from commuter data. Modelling is based on diffusion approximations derived in Chap. 5. Statistical inference is carried out using a Bayesian approach developed in Chap. 7.

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References

  • Baroyan O, Rvachev L (1967) Deterministic epidemic models for a territory with a transport network (in Russian). Kibernetika 3:67–74

    Google Scholar 

  • Baroyan O, Rvachev L, Ivannikov Y (1977) Modelling and forecasting of influenza epidemics for territory of the USSR (in Russian). Gamelaya Institute of Epidemiology and Microbiology, Moscow

    Google Scholar 

  • BMJ News and Notes (1978) Influenza in a boarding school. Br Med J 1:587

    Google Scholar 

  • Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature 439:462–465

    Article  Google Scholar 

  • Brownstein J, Wolfe C, Mandl K (2006) Empirical evidence for the effect of airline travel on inter-regional influenza spread in the United States. PLoS Med 3:1826–1835

    Google Scholar 

  • Cauchemez S, Ferguson N, Wachtel C, Tegnell A, Saour G, Duncan B, Nicoll A (2009) Closure of schools during an influenza pandemic. Lancet Infect Dis 9:473–81

    Article  Google Scholar 

  • Chen WY, Bokka S (2005) Stochastic modeling of nonlinear epidemiology. J Theor Biol 234: 455–470

    Article  MathSciNet  Google Scholar 

  • Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and hpd intervals. J Comput Graph Stat 8:69–92

    MathSciNet  Google Scholar 

  • Colizza V, Barrat A, Barthélemy M, Vespignani A (2006a) The modeling of global epidemics: stochastic dynamics and predictability. Bull Math Biol 68:1893–1921

    Article  MathSciNet  Google Scholar 

  • Colizza V, Barrat A, Barthélemy M, Vespignani A (2006b) The role of the airline transportation network in the prediction and predictability of global epidemics. Proc Natl Acad Sci USA 103:2015–2020

    Article  Google Scholar 

  • Crépey P, Barthélemy M (2007) Detecting robust patterns in the spread of epidemics: a case study of influenza in the United States and France. Am J Epidemiol 166:1244–1251

    Article  Google Scholar 

  • Dushoff J, Plotkin J, Levin S, Earn D (2004) Dynamical resonance can account for seasonality of influenza epidemics. Proc Natl Acad Sci U S A 101:16915–16916

    Article  Google Scholar 

  • Ginsberg J, Mohebbi M, Patel R, Brammer L, Smolinski M, Brilliant L (2008) Detecting influenza epidemics using search engine query data. Nature 457:1012–1014

    Article  Google Scholar 

  • Grais R, Ellis J, Glass G (2003) Assessing the impact of airline travel on the geographic spread of pandemic influenza. Eur J Epidemiol 18:1065–1072

    Article  Google Scholar 

  • Hufnagel L, Brockmann D, Geisel T (2004) Forecast and control of epidemics in a globalized world. Proc Natl Acad Sci U S A 101:15124–15129

    Article  Google Scholar 

  • Keeling M, Rohani P (2008) Modeling infectious disease in humans and animals. Princeton University Press, Princeton

    Google Scholar 

  • Medlock J, Galvani A (2009) Optimizing influenza vaccine distribution. Sci Express 10.1126/science.1175570:1–9

    MATH  Google Scholar 

  • Murray J (2002) Mathematical biology: I. an introduction, 3rd edn. Interdisciplinary applied mathematics. Springer, Berlin/Heidelberg

    Google Scholar 

  • Nelder J, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313

    Article  MATH  Google Scholar 

  • Russell C, Jones T, Barr I, Cox N, Garten R, Gregory V, Gust I, Hamson A (2008) The global circulation of seasonal influenza A (H3N2) viruses. Science 320:340–346

    Article  Google Scholar 

  • Rvachev L, Longini I (1985) A mathematical model for the global spread of influenza. Math Biosci 75:3–22

    Article  MathSciNet  MATH  Google Scholar 

  • Sattenspiel L (2009) The geographic spread of infectious diseases: models and applications. Princeton University Press, Princeton

    Google Scholar 

  • Stephenson I, Nicholson K (2001) Influenza: vaccination and treatment. Eur Respir J 17: 1281–1293

    Article  Google Scholar 

Download references

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Fuchs, C. (2013). Application I: Spread of Influenza. In: Inference for Diffusion Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25969-2_8

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