Cite

[1] H. Andersson and T. Britton, Stochastic Epidemic Models and Their Statistical Analysis. Springer-Verlag, New York (2000).10.1007/978-1-4612-1158-7 Search in Google Scholar

[2] N,T,J. Bailey, The Mathematical Theory of Infectious Diseases and Its Application. 2nd edition, Hafner Press, New York (1975). Search in Google Scholar

[3] N.G. Becker, On a general stochastic epidemic model, Theoretical Population Biology, 11 (1976), 23-26.10.1016/0040-5809(77)90004-1 Search in Google Scholar

[4] S.P. Blythe, F. Brauer and C. Castillo-Chavez, Demographic recruitment in sexually transmitted disease models, Proc. First World Congress on Computational Medicine, Public Health and Biotechnology Part II Austin, TX, 1994. Ed. Matthew Witten. Series in Mathematical Biology and Medicine 5 (1997), 1438-1457. Search in Google Scholar

[5] S.P. Blythe, F. Brauer, C. Castillo-Chavez and J. Velasco-Hernandez, Models for sexuality transmitted diseases with recruitment. Biometrics Unit Technical Report BU-1193-M, Cornell University (1995). Search in Google Scholar

[6] B. Choi and G.A. Rempala, Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling, Biostatistics, 13(1) (2012), 153-165.10.1093/biostatistics/kxr019327627221835814 Search in Google Scholar

[7] D. Clancy, P.D. O’Neill et al, Bayesian estimation of the basic reproduction number in stochastic epidemic models, Bayesian Analysis, 3(4) (2008), 737-757.10.1214/08-BA328 Search in Google Scholar

[8] R.T. Clarke, Bivariate gamma distributions for extending annual stream flow records from precipitation, Water Resources Research, 16 (1980), 863-870.10.1029/WR016i005p00863 Search in Google Scholar

[9] N.Demiris and P.D. O’Neill, Computation of final outcome probabilities for the generalised stochastic epidemic, Stat Comput, 16 (2006), 309-317.10.1007/s11222-006-8320-4 Search in Google Scholar

[10] N. Demiris and P.D. O’Neill, Bayesian inference for epidemics with two levels of mixing, Scand. J. Stat, 32 (2005a), 265-280.10.1111/j.1467-9469.2005.00420.x Search in Google Scholar

[11] N. Demiris and P.D. O’Neill, Bayesian inference for stochastic multitype epidemics in structured populations via random graphs, J. Roy. Statist. Soc. B, 67 (2005b, 731-745.10.1111/j.1467-9868.2005.00524.x Search in Google Scholar

[12] H. El Maroufy, D. Kiouach, T. Ziad, Final outcome probabilities for SIR epidemic model, Communication in Statistics-Theory and Methods (2016).10.1080/03610926.2014.881494 Search in Google Scholar

[13] H. El Maroufy, T. Kernane, S. Bechket and A. Ouddaj, Bayesian Inference for Non Linear Stochastic SIR Epidemic Model, Journal of Statistical Computation and Simulation (2015).10.1080/00949655.2015.1107561 Search in Google Scholar

[14] H. El Maroufy, L. Omari, T. Ziad, Transition Probabilities for Generalized SIR Epidemic Model, Stochastic Model (2012).10.1080/15326349.2011.614201 Search in Google Scholar

[15] Bjørn. Eraker, MCMC Analysis of Diffusion Models With Application to Finance, Journal of Business and Economic Statistics, 19 (2001), 177-191.10.1198/073500101316970403 Search in Google Scholar

[16] P. Fearnhead and L. Meligkotsidou, Exact filtering for partially-observed continuous time models, Journal of the Royal Statistical Society. B, 66 (2004), 771-789.10.1111/j.1467-9868.2004.05561.x Search in Google Scholar

[17] C. Fuchs, Inference for diffusion process: with application in life sciences. Springer-Verlag, Berlin (2013).10.1007/978-3-642-25969-2 Search in Google Scholar

[18] G.J. Gibson and E. Renshaw, Estimating parameters in stochastic compartmental models using Markov chain methods, Journal of Mathematics in Applied Medicine and Biology, 15 (1998), 19-40.10.1093/imammb/15.1.19 Search in Google Scholar

[19] T. Izawa, Two or multi-dimensional gamma-type distribution and its application to rainfall data, Papers in Meteorology and Geophysics, (1965), 167.10.2467/mripapers1950.15.3-4_167 Search in Google Scholar

[20] W.F. Kibble, A two-variate gamma type distribution, Sankhya, 5 (1941), 137-150. Search in Google Scholar

[21] M. Komorowski, M.J. Costa, D.A. Rand and M.PH. Stumpf, Sensitivity, robustness, and identifiability in stochastic chemical kinetics models, Proceedings of the National Academy of Sciences, 108(21) (2011), 8645-8650.10.1073/pnas.1015814108 Search in Google Scholar

[22] P.E. Lekone and B.F. Roberts, Statistical inference and model selection for the 1861 Hagelloch measles epidemic, Biostatistics, 5 (2004), 249-261.10.1093/biostatistics/5.2.249 Search in Google Scholar

[23] A.M. Mathai, P.G. Moschopoulos, On a multivariate gamma, Journal of Multivariate Analysis, Journal of Multivariate Analysis, 39 (1991), 135-153.10.1016/0047-259X(91)90010-Y Search in Google Scholar

[24] P.A.P. Moran, Statistical inference with bivariate gamma distributions, Biometrika, 54 (1969), 385-394.10.1093/biomet/54.3-4.385 Search in Google Scholar

[25] P.A.P. Moran, The methodology of rain making experiments, Review of the International Statistical Institute, 38 (1970), 105-115.10.2307/1402327 Search in Google Scholar

[26] P.J. Neal and G.O. Wilkinson, Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation, Biometrics, 61 (2005), 781-788.10.1111/j.1541-0420.2005.00345.x16135029 Search in Google Scholar

[27] P,D. O’Neill and G,O. Roberts, Bayesian inference for partially observed stochastic epidemics, J.R.S.S, Series A, 162 (1999), 121-129.10.1111/1467-985X.00125 Search in Google Scholar

[28] A. Pedersen, A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observation, Scandinavian Journal of Statistics, 22 (1995), 55-71. Search in Google Scholar

[29] A. Qaffou, H. El Maroufy and T. Kernane, Bayesian Parameter Inference for Stochastic SIR Epidemic Model with Hyperbolic Diffusion, Communications in Statistics-Simulation and Computation, 46 (2017), 69076922.10.1080/03610918.2016.1217013 Search in Google Scholar

[30] H. Risken, Fokker-Plank Equation, Method of Solution and Application. Second-edition, Springer-Verlag, New York (1989).10.1007/978-3-642-61544-3 Search in Google Scholar

[31] O.E. Smith, S.I. Adelfang, Gust model based on the bivariate gamma distribution, Journal of Spacecraft, 18 (1981), 545-549.10.2514/3.57850 Search in Google Scholar

[32] G. Streftaris and G.J. Gibson, Bayesian inference for stochastic epidemics in closed populations, Statistical Modelling (2004).10.1191/1471082X04st065oa Search in Google Scholar

[33] D.J. Woodcock, M. Komorowski, B. Finkenstadt, C.V. Harper, J. Davis, M.RH. White and D.A. Rand, A bayesian hierarchical diffusion model for estimating kinetic parameters and cell-to-cell variability. Warwick Uni working Paper (2011). Search in Google Scholar

eISSN:
2351-8227
Idioma:
Inglés