Bayesian Inference for SIR Epidemic Model with dependent parameters
References
- [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
- [2] N,T,J. Bailey, The Mathematical Theory of Infectious Diseases and Its Application. 2nd edition, Hafner Press, New York (1975).
- [3] N.G. Becker, On a general stochastic epidemic model, Theoretical Population Biology, 11 (1976), 23-26.10.1016/0040-5809(77)90004-1
- [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.
- [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).
- [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
- [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
- [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
- [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
- [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
- [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
- [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
- [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
- [14] H. El Maroufy, L. Omari, T. Ziad, Transition Probabilities for Generalized SIR Epidemic Model, Stochastic Model (2012).10.1080/15326349.2011.614201
- [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
- [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
- [17] C. Fuchs, Inference for diffusion process: with application in life sciences. Springer-Verlag, Berlin (2013).10.1007/978-3-642-25969-2
- [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
- [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
- [20] W.F. Kibble, A two-variate gamma type distribution, Sankhya, 5 (1941), 137-150.
- [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
- [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
- [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
- [24] P.A.P. Moran, Statistical inference with bivariate gamma distributions, Biometrika, 54 (1969), 385-394.10.1093/biomet/54.3-4.385
- [25] P.A.P. Moran, The methodology of rain making experiments, Review of the International Statistical Institute, 38 (1970), 105-115.10.2307/1402327
- [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
- [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
- [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.
- [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
- [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
- [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
- [32] G. Streftaris and G.J. Gibson, Bayesian inference for stochastic epidemics in closed populations, Statistical Modelling (2004).10.1191/1471082X04st065oa
- [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).
DOI: https://doi.org/10.2478/mjpaa-2022-0017 | Journal eISSN: 2351-8227
Language: English
Page range: 244 - 255
Submitted on: Feb 10, 2021
Accepted on: Apr 3, 2022
Published on: May 28, 2022
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
Keywords:
Related subjects:
© 2022 Abdelaziz Qaffou, Hamid El Maroufy, Mokhtar Zbair, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.