Bayesian melding estimation of a stochastic SEIR model

Mathematical Population Studies

Volumn 17, Issue 2, 2010, Pages 101-111

  Hotta, Luiz K ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Bayesian inference; Bayesian melding; HIV TB interaction; SEIR model estimation; Stochastic epidemic models; Stochastic SEIR model

Indexed keywords

BAYESIAN ANALYSIS; ESTIMATION METHOD; HUMAN IMMUNODEFICIENCY VIRUS; LEAST SQUARES METHOD; TUBERCULOSIS;

EID: 77951678076     PISSN: 08898480     EISSN: 1547724X     Source Type: Journal    
DOI: 10.1080/08898481003689528     Document Type: Article

References (24)

1. Alkema, L., Raftery, A.E., and Clark, S.J. (2007). Probabilistic projections of HIV prevalence using Bayesian melding. The Annals of Applied Statistics, 1(1): 229-248.
2. Anderson, R.M. and May, R.M. (1991). Infectious Diseases of Humans. Oxford, UK: Oxford University Press.
3. Andersson, H. (1999). Epidemic models and social networks. Mathematical Scientist, 24(2): 128-147.
4. Ades, A.E. and Cliffe, S. (2002). Markov chain Monte Carlo estimation of a multiparameter decision model: Consistency of evidence and the accurate assessment of uncertainty. Medical Decision Making, 22(4): 359-371.
5. Bailey, N.T.J. (1975). The Mathematical Theory of Infectious Diseases and Applications (2nd Edition). London: Griffin.
6. Boys, R.J. and Giles, P.R. (2007). Bayesian inference for SEIR epidemic models with time-inhomogeneous removal rates. Journal of Mathematical Biology, 55(2): 223-247.
7. Brookhart, M.A., Hubbard, A.E., van der Laan, M.J., Colford, J.M., and Eisenberg, N.S. (2002). Statistical estimation of parameters in a disease transmission model: Analysis of a cryptosporidium outbreak. Statistics in Medicine, 21(23): 3627-3638.
8. Cancré, N., Tall, A., Rogier, C., Faye, J., Sarr, O., Trape, J.-F., et al. (2000). Bayesian analysis of an epidemiological model of Plasmodium falciparum malaria infection in Ndiop, Senegal. American Journal of Epidemiology, 152(8): 760-770.
9. Chowell, G., Hengartner, N.W., Castillo-Chavez, C., Fenimore, P.W., and Hyman, J. M. (2004). The basic reproductive number of Ebola and the effects of public health measures: The cases of Congo and Uganda. Journal of Theoretical Biology, 229(1): 119-126.
10. Ferreira, M.A.C., Ferrazoli, L., Palaci, M., Salles, P.S., Medeiros, L.A., Novoa, P., et al. (1996). Tuberculosis among HIV infected women inmates in São Paulo, Brazil: A prospective cohort study. Journal of AIDS and Human Retrovirology, 13(2): 177-183.
11. Lekone, P.E. and Finkenstadt, B.F. (2006). Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics, 62(4): 1170-1177.
12. Marino, S. and Kirschner, D. (2003). The human immune response to Mycobacterium tuberculosis in lung and lymph node. Journal of Theoretical Biology, 227(4): 463-486.
13. Massad, E., Burattini, M.N., Coutinho, F.A.B., Yang, H.M., and Raimundo, S.M. (1993). Modeling the interaction between AIDS and tuberculosis. Mathematical Computing Modeling, 17(9): 7-22.
14. Neal, P.J. and Roberts, G.O. (2004). Statistical inference and model selection for the Hagelloch measles epidemic. Biostatistics, 5(2): 249-261.
15. O'Neill, P.D. (2002). A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods. Mathematical Biosciences, 80(1-2): 103-114.
16. O'Neill, P.D. and Roberts, G.O. (1999). Bayesian inference for partially observed stochastic epidemics. Journal of the Royal Statistical Society, Series B, 162(1): 121-129.
17. Poole, D. and Raftery, A.E. (2000). Inference for deterministic simulation models: The Bayesian melding approach. Journal of the American Statistical Association, 95(452): 1244-1255.
18. Raftery, A.E., Givens, G.H., and Zeh, J.E. (1995). Inference from a deterministic population dynamics model for bowhead whales (with discussion). Journal of the American Statistical Association, 90(430): 402-416.
19. Raimundo, S.M., Engel, A.B., Yang, H.M., and Bazzanezi, R. (2003). An approach to estimating the transmission coefficients for AIDS for tuberculosis using mathematical models. Systems Analysis Modeling Simulation, 43(4): 423-442.
20. Raimundo, S.M., Yang, H.M., Bazzanezi, R.C., and Ferreira, M.A.C. (2002). The attracting basins and the assessment of the transmission coefficients for HIV and M. tuberculosis infections among women inmates. Journal of Biological Systems, 10(1): 61-83.
21. Rubin, D. (1987). Comment on the calculation of posterior distributions by data augmentation, by M. Tanner and W.H. Wang. Journal of the American Statistical Association, 82(398): 543-546.
22. Rubin, D. (1988). Using the SIR algorithm to simulate posterior distributions. In J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith (Eds.), Bayesian Statistics 3. Oxford, UK: Clarendon Press, pp. 395-402.
23. Streftaris, G. and Gibson, G.J. (2004). Bayesian inference for stochastic epidemics in closed population. Statistical Modeling, 4(1): 63-75.
24. Wigginton, J.W. and Kirschner, D. (2001). A model to predict cell-mediated immune regulatory mechanisms during human infection with Mycobacterium tuberculosis. The Journal of Immunology, 166: 1951-1967.