Multi-species SIR models from a dynamical Bayesian perspective

Theoretical Ecology

Volumn 6, Issue 4, 2013, Pages 457-473

  Zhuang, Lili ^a   Cressie, Noel ^b   Pomeroy, Laura ^a   Janies, Daniel ^c  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WOLLONGONG   (Australia)

^c University of North Carolina at Charlotte   (United States)

Author keywords

Disease dynamics; Epidemic model; HSIR; Influenza; Mass balance; MSIR

Indexed keywords

BAYESIAN ANALYSIS; DISEASE SPREAD; INFLUENZA; MASS BALANCE; NUMERICAL MODEL; STOCHASTICITY; UNCERTAINTY ANALYSIS;

EID: 84886778090     PISSN: 18741738     EISSN: 18741746     Source Type: Journal    
DOI: 10.1007/s12080-013-0180-x     Document Type: Article

References (42)

1. Alexander DJ (2000) A review of avian influenza in different bird species. Vet Microbiol 74: 3-13.
2. Allen L (2003) An introduction to stochastic processes with applications to biology. Prentice-Hall, Upper Saddle River.
3. Alonso D, McKane AJ, Pascual M (2007) Stochastic amplification in epidemics. J R Soc Interface 4(14): 575-582.
4. Anderson R, May R (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford.
5. Arino J (2009) Diseases in metapopulations. In: Ma Z, Zhou Y, Wu J (eds) Series in contemporary applied mathematics, vol 11. World Scientific, Singapore, pp 65-123.
6. Arino J, Davis J, Hartley D, Jordan R, Miller J, van Den Driessche P (2005) A multi-species epidemic model with spatial dynamics. Math Med Biol 22: 129-142.
7. Arulampalam S, Maskell S, Gordon N, Clapp T (2001) A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50: 174-188.
8. Besag J, York J, Mollié A (1991) Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math 43: 1-59.
9. Black AJ, McKane AJ (2010) Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough. J R Soc Interface 7: 1219-1227.
10. Bouma A, Claassen I, Natih K, Klinkenberg D, Donnelly C, Koch G, van Boven M (2009) Estimation of transmission parameters of H5N1 avian influenza virus in chickens. PLOS Pathogens 5(1): e1000, 281.
11. Carlin B, Banerjee S (2002) Hierarchical multivariate CAR models for spatio-temporally correlated survival data (with discussion). In: Bernardo J, Bayarri M, Berger J, Dawid A, Heckerman D, Smith AFM, West M (eds) Bayesian statistics, vol 7. Clarendon Press, Oxford, pp 45-63.
12. Cressie N, Wikle C (2011) Statistics for spatio-temporal data. Wiley, Hoboken.
13. Dobson A (2004) Population dynamics of pathogens with multiple host species. Am Nat 164: S64-S78.
14. Dukić V, V, Lopes HF, Polson NG (2009) Tracking epidemics with Google flu trends data and a state-space SEIR model. J Am Stat Assoc 107: 1410-1426.
15. Ellner SP, Bailey BA, Bobashev GV, Gallant AR, Grenfell BT, Nychka DW (1998) Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. Am Nat 151(5): 425-440.
16. He D, Ionides EL, King AA (2010) Plug-and-play inference for disease dynamics: measles in large and small populations as a case study. J R Soc Interface 7: 271-283.
17. Hethcote HW (2000) The mathematics of infectious diseases. SIAM Review 42: 599-653.
18. Hooten MB, Wikle CK (2010) Statistical agent-based models for discrete spatio-temporal systems. J Am Stat Assoc 105: 236-248.
19. Ionides EL, Bretó C, King AA (2006) Inference for nonlinear dynamical systems. Proc Natl Acad Sci U. S. A. 103: 18, 438-18, 443.
20. Jenkinson G, Goutsias J (2012) Numerical integration of the master equation in some models of stochastic epidemiology. PLoS ONE 7: e36, 160.
21. Kendall BE, Briggs CJ, Murdoch WW, Turchin P, Ellner SP, McCauley E, Nisbet RM, Wood SN (1999) Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology 80: 1789-1805.
22. Kendall BE, Ellner SP, McCauley E, Wood SN, Briggs CJ, Murdoch WM, Turchin P (2005) Population cycles in the pine looper moth: dynamical tests of mechanistic hypotheses. Ecol Monogr 75: 259-276.
23. Kermack W, McKendrick A (1927) Contributions to the mathematical theory of epidemics. Proc R Soc Edinb A 115: 700-721.
24. King AA, Ionides EL, Pascual M, Bouma MJ (2008) Inapparent infections and cholera dynamics. Nature 454: 877-880.
25. Kuiken T, Holmes E, McCauley J, Rimmelzwaan G, Williams C, Grenfell B (2006) Host species barriers to influenza virus infections. Science 312: 394-397.
26. Liu J, West M (2001) Combined parameter and state estimation in simulation-based filtering. In: Doucet A, de Freitas N, Gordon NJ (eds) Sequential Monte Carlo methods in practice. Springer, New York, pp 197-224.
27. Mugglin A, Cressie N, Gemmell I (2002) Hierarchical statistical modelling of influenza epidemic dynamics in space and time. Stat Med 21: 2703-2721.
28. Munster V, Baas C, Lexmond P, Waldenström J, Wallensten A, Fransson T, Rimmelzwaan GF, Beyer WEP, Schutten M, Olsen B, Osterhaus ADME, Fouchier RAM (2007) Spatial, temporal, and species variation in prevalence of influenza A viruses in wild migratory birds. PLoS Pathog 3: e61.
29. Nelson MI, Holmes EC (2007) The evolution of epidemic influenza. Nat Rev Genet 8: 196-205.
30. Nelson MI, Vincent AL, Kitikoon P, Holmes EC, Gramer MR (2012) Evolution of novel reassortant A/H3N2 influenza viruses in North American swine and humans, 2009-2011. J Virol 86(16): 8872-8878.
31. Reed C, Angulo FJ, Swerdlow DL, Lipsitch M, Meltzer MI, Jernigan D, Finelli L (2009) Estimates of the prevalence of pandemic H1N1 2009, United States, April-July 2009. Emerg Infect Dis 15: 2004-2007.
32. Reluga T (2004) A two-phase epidemic driven by diffusion. J Theor Biol 229: 249-261.
33. Saenz RA, Hethcote HW, Gray GC (2006) Confined animal feeding operations as amplifiers of influenza. Vector Borne Zoonotic Dis 6: 338-346.
34. Scholtissek C (1990) Pigs as the 'mixing vessels' for the creation of new pandemic influenza A viruses. Med Princ Pract 2: 65-71.
35. Stallknecht DE, Brown JD (2007) Wild birds and the epidemiology of avian influenza. J Wildl Dis 43: S15-S20.
36. Vincent A, Ma W, Lager K, Janke B, Richt J (2008) Swine influenza viruses: a North American perspective. Adv Virus Res 72: 127-154.
37. Waller L, Carlin B, Xia H, Gelfand A (1997) Hierarchical spatio-temporal mapping of disease rates. J Am Stat Assoc 92: 607-617.
38. Webby RJ, Webster RG, Richt JA (2007) Influenza viruses in animal wildlife populations. Curr Top Microbiol Immunol 315: 67-83.
39. Webster RG, Bean WJ, Gorman OT, Chambers TM, Kawaoka Y (1992) Evolution and ecology of influenza A viruses. Microbiol Mol Biol Rev 56: 152-179.
40. Wood SN (2010) Statistical inference for noisy nonlinear ecological dynamic systems. Nature 466: 1102-1104.
41. Xu Y, Allena L, Perelson A (2007) Stochastic model of an influenza epidemic with drug resistance. J Theor Biol 248: 179-193.
42. Zhuang L (2011) Bayesian dynamical modeling of count data. PhD thesis, Department of Statistics, The Ohio State University. http://rave. ohiolink. edu/etdc/view?acc_num=osu1315949027.