1932

Abstract

This article considers simulation and analysis of incidence data using stochastic compartmental models in well-mixed populations. Several simulation approaches are described and compared. Thereafter, we provide an overview of likelihood estimation for stochastic models. We apply one such method to a real-life outbreak data set and compare models assuming different kinds of stochasticity. We also give references for other publications where detailed information on this topic can be found.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-statistics-061120-034438
2021-03-07
2024-06-14
Loading full text...

Full text loading...

/deliver/fulltext/statistics/8/1/annurev-statistics-061120-034438.html?itemId=/content/journals/10.1146/annurev-statistics-061120-034438&mimeType=html&fmt=ahah

Literature Cited

  1. Allen LJS. 2017. A primer on stochastic epidemic models: formulation, numerical simulation, and analysis. Infect. Dis. Model. 2:128–42
    [Google Scholar]
  2. Anderson RM, May RM. 1992. Infectious Diseases of Humans: Dynamics and Control Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  3. Andersson H, Britton T. 2000. Stochastic Epidemic Models and Their Statistical Analysis New York: Springer
    [Google Scholar]
  4. Bailey NTJ. 1955. Some problems in the statistical analysis of epidemic data. J. R. Stat. Soc. Ser. B 17:35–58
    [Google Scholar]
  5. Bartlett MS. 1957. Measles periodicity and community size. J. R. Stat. Soc. Ser. A 120:48–70
    [Google Scholar]
  6. Bartlett MS. 1960. Stochastic Population Models in Ecology and Epidemiology London: Methuen
    [Google Scholar]
  7. Bartlett MS. 1961. Monte Carlo studies in ecology and epidemiology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability J Neyman 39–55 Berkeley: Univ. Calif. Press
    [Google Scholar]
  8. Beaumont MA. 2019. Approximate Bayesian computation. Annu. Rev. Stat. Appl. 6:379–403
    [Google Scholar]
  9. Brauer F, Castillo-Chávez C. 2001. Mathematical Models in Population Biology and Epidemiology New York: Springer
    [Google Scholar]
  10. Bretó C. 2018. Modeling and inference for infectious disease dynamics: a likelihood-based approach. Stat. Sci. Rev. J. Inst. Math. Stat. 33:57–69
    [Google Scholar]
  11. Bretó C, He D, Ionides EL, King AA 2009. Time series analysis via mechanistic models. Ann. Appl. Stat. 3:319–48
    [Google Scholar]
  12. Chao DL, Halloran ME, Obenchain VJ, Longini IM Jr 2010. FluTE, a publicly available stochastic influenza epidemic simulation model. PLOS Comput. Biol. 6:1e1000656
    [Google Scholar]
  13. Chowell G. 2017. Fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer for parameter uncertainty, identifiability, and forecasts. Infect. Dis. Model. 2:379–98
    [Google Scholar]
  14. Chowell G, Hyman JM, Bettencourt LMA, Castillo-Chavez C 2009. Mathematical and Statistical Estimation Approaches in Epidemiology New York: Springer
    [Google Scholar]
  15. Chowell G, Nishiura H, Bettencourt LM 2007. Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J. R. Soc. Interface 4:155–66
    [Google Scholar]
  16. Claeskens G, Hjort NL. 2008. Model Selection and Model Averaging Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  17. Coburn BJ, Wagner BG, Blower S 2009. Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1). BMC Med 7:30
    [Google Scholar]
  18. Coulson T, Rohani P, Pascual M 2004. Skeletons, noise and population growth: the end of an old debate. ? Trends Ecol. Evol. 19:359–64
    [Google Scholar]
  19. Csilléry K, Blum MG, Gaggiotti OE, François O 2010. Approximate Bayesian computation (ABC) in practice. Trends Ecol. Evol. 25:410–18
    [Google Scholar]
  20. Daley DJ, Gani J. 2001. Epidemic Modelling: An Introduction Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  21. Diekmann O, Heesterbeek JAP, Metz JAJ 1990. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28:365–82
    [Google Scholar]
  22. Dong E, Du H, Gardner L 2020. An interactive web-based dashboard to track COVID-19 in real time. Lancet Infect. Dis. 20:533–34
    [Google Scholar]
  23. Eberhard P, Schiehlen W, Bestle D 1999. Some advantages of stochastic methods in multicriteria optimization of multibody systems. Arch. Appl. Mech. Ing. Arch. 69:543–54
    [Google Scholar]
  24. Fasiolo M, Pya N, Wood SN 2016. A comparison of inferential methods for highly nonlinear state space models in ecology and epidemiology. Stat. Sci. 31:96–118
    [Google Scholar]
  25. Fuchs C. 2013. Inference for Diffusion Processes: With Applications in Life Sciences New York: Springer
    [Google Scholar]
  26. Fujiwara M, Takada T. 2001. Environmental stochasticity. eLS https://doi.org/10.1002/9780470015902.a0021220.pub2
    [Crossref] [Google Scholar]
  27. Ganyani T, Faes C, Chowell G, Hens N 2018. Assessing inference of the basic reproduction number in an SIR model incorporating a growth-scaling parameter. Stat. Med. 37:4490–506
    [Google Scholar]
  28. Ganyani T, Faes C, Hens N 2020. Inference of the generalized-growth model via maximum likelihood estimation: a reflection on the impact of overdispersion. J. Theor. Biol. 484:110029
    [Google Scholar]
  29. Gibson GJ, Renshaw E. 1998. Estimating parameters in stochastic compartmental models using Markov chain methods. Math. Med. Biol. 15:19–40
    [Google Scholar]
  30. Gibson GJ, Renshaw E. 2001. Likelihood estimation for stochastic compartmental models using Markov chain methods. Stat. Comput. 11:347–58
    [Google Scholar]
  31. Gillespie DT. 1977. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81:2340–61
    [Google Scholar]
  32. Gillespie DT. 2001. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115:1716–33
    [Google Scholar]
  33. Halloran ME, Auranen K, Baird S, Basta NE, Bellan SE et al. 2017. Simulations for designing and interpreting intervention trials in infectious diseases. BMC Med 15:223
    [Google Scholar]
  34. Heesterbeek H. 2005. The law of mass-action in epidemiology: a historical perspective. Ecological Paradigms Lost: Routes of Theory Change K Cuddington, B Beisner 81–104 Amsterdam: Elsevier
    [Google Scholar]
  35. Held L, Hens N, O'Neill PD, Wallinga J 2019. Handbook of Infectious Disease Data Analysis Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  36. Hens N, Shkedy Z, Aerts M, Faes C, Damme PV, Beutels P 2012. Modeling Infectious Disease Parameters Based on Serological and Social Contact Data New York: Springer
    [Google Scholar]
  37. Hollingsworth TD. 2009. Controlling infectious disease outbreaks: lessons from mathematical modelling. J. Public Health Policy 30:328–41
    [Google Scholar]
  38. Hunter E, Mac Namee B, Kelleher JD 2017. A taxonomy for agent-based models in human infectious disease epidemiology. J. Artif. Soc. Soc. Simul. 20:32
    [Google Scholar]
  39. Ionides EL, Bretó C, King AA 2006. Inference for nonlinear dynamical systems. PNAS 103:18438–43
    [Google Scholar]
  40. Kaminsky J, Keegan LT, Metcalf CJE, Lessler J 2019. Perfect counterfactuals for epidemic simulations. Philos. Trans. R. Soc. B 374:20180279
    [Google Scholar]
  41. Keeling MJ, Eames KT. 2005. Networks and epidemic models. J. R. Soc. Interface 2:295–307
    [Google Scholar]
  42. Keeling MJ, Rohani P. 2008. Modeling Infectious Diseases in Humans and Animals Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  43. Keeling MJ, Ross JV. 2009. Efficient methods for studying stochastic disease and population dynamics. Theor. Popul. Biol. 75:133–41
    [Google Scholar]
  44. Kermack WO, McKendrick AG. 1927. Contributions to the mathematical theory of epidemics. Part I. Proc. R. Soc. Ser. A 115:700–21
    [Google Scholar]
  45. King AA, de Cellès MD, Magpantay FMG, Rohani P 2015. Avoidable errors in the modelling of outbreaks of emerging pathogens, with special reference to Ebola. Proc. R. Soc. Ser. B 282:20150347
    [Google Scholar]
  46. King AA, Ionides EL, Asfaw K 2018. Simulation-based inference for epidemiological dynamics. Presented at Summer Institute in Statistics and Modeling in Infectious Diseases. . https://kingaa.github.io/sbied/
    [Google Scholar]
  47. King AA, Nguyen D, Ionides EL 2016. Statistical inference for partially observed Markov processes via the R package pomp. J. Stat. Softw. 69:12
    [Google Scholar]
  48. Kypraios T, Minin VN. 2018. Introduction to the Special Section on Inference for Infectious Disease Dynamics. Stat. Sci. 33:1–3
    [Google Scholar]
  49. Kypraios T, Neal P, Prangle D 2017. A tutorial introduction to Bayesian inference for stochastic epidemic models using approximate Bayesian computation. Math. Biosci. 287:42–53
    [Google Scholar]
  50. Lekone PE, Finkenstädt BF. 2006. Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62:1170–77
    [Google Scholar]
  51. Li M, Dushoff J, Bolker BM 2018. Fitting mechanistic epidemic models to data: a comparison of simple Markov chain Monte Carlo approaches. Stat. Methods Med. Res. 27:1956–67
    [Google Scholar]
  52. Mandal S, Sarkar R, Sinha S 2011. Mathematical models of malaria—a review. Malaria J 10:202
    [Google Scholar]
  53. McCallum H. 2001. How should pathogen transmission be modelled. ? Trends Ecol. Evol. 16:295–300
    [Google Scholar]
  54. McKinley TJ, Vernon I, Andrianakis I, McCreesh N, Oakley JE et al. 2018. Approximate Bayesian computation and simulation-based inference for complex stochastic epidemic models. Stat. Sci. 33:4–18
    [Google Scholar]
  55. Mood AM, Graybill FA, Boes DC 1950. Introduction to the Theory of Statistics New York: McGraw–Hill
    [Google Scholar]
  56. Nadeem K, Moore JE, Zhang Y, Chipman H 2016. Integrating population dynamics models and distance sampling data: a spatial hierarchical state-space approach. Ecology 97:1735–45
    [Google Scholar]
  57. Newman ME. 2002. Spread of epidemic disease on networks. Phys. Rev. E 66:016128
    [Google Scholar]
  58. O'Neill PD. 2010. Introduction and snapshot review: relating infectious disease transmission models to data. Stat. Med. 29:2069–77
    [Google Scholar]
  59. O'Neill PD, Roberts GO. 1999. Bayesian inference for partially observed stochastic epidemics. J. R. Stat. Soc. Ser. A 162:121–29
    [Google Scholar]
  60. Ozcaglar C, Shabbeer A, Vandenberg SL, Yener B, Bennett KP 2012. Epidemiological models of Mycobacterium tuberculosis complex infections. Math. Biosci. 236:77–96
    [Google Scholar]
  61. Pineda-Krch M. 2008. GillespieSSA: implementing the stochastic simulation algorithm in R. J. Stat. Softw. 25:12
    [Google Scholar]
  62. Railsback SF, Grimm V. 2011. Agent-Based and Individual-Based Modeling: A Practical Introduction Princeton, NJ: Princeton Univ. Press
    [Google Scholar]
  63. Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M et al. 2009. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25:1923–29
    [Google Scholar]
  64. Ross SM. 2014. Introduction to Probability Models New York: Academic
    [Google Scholar]
  65. Stocks T, Britton T, Höhle M 2020. Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany. Biostatistics 23:3400–16
    [Google Scholar]
  66. Taubenberger JK, Morens DM. 2006. 1918 influenza: the mother of all pandemics. Rev. Biomed. 17:69–79
    [Google Scholar]
  67. Tuncer N, Le TT. 2018. Structural and practical identifiability analysis of outbreak models. Math. Biosci. 299:1–18
    [Google Scholar]
  68. Van Dyk DA, Meng XL 2001. The art of data augmentation. J. Comput. Graph. Stat. 10:1–50
    [Google Scholar]
  69. Wilkinson DJ. 2018. Stochastic Modelling for Systems Biology Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
/content/journals/10.1146/annurev-statistics-061120-034438
Loading
/content/journals/10.1146/annurev-statistics-061120-034438
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error