C. Safta, J. Ray, S. Lefantzi, D. Crary, K. Sargsyan, K. Cheng
We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiological parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.
{"title":"Real-time characterization of partially observed epidemics using surrogate models.","authors":"C. Safta, J. Ray, S. Lefantzi, D. Crary, K. Sargsyan, K. Cheng","doi":"10.2172/1030325","DOIUrl":"https://doi.org/10.2172/1030325","url":null,"abstract":"We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiological parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125167386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-07-31DOI: 10.1016/J.MBS.2006.12.001
B. Snel
{"title":"Computational Genome Analysis: An Introduction, R.C. Deonier, S. Tavare, M.S. Waterman. Springer, New York (2004), 555 pp., GBP 5000, ISBN: 0387987851","authors":"B. Snel","doi":"10.1016/J.MBS.2006.12.001","DOIUrl":"https://doi.org/10.1016/J.MBS.2006.12.001","url":null,"abstract":"","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128387563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2001-02-01DOI: 10.1016/S0025-5564(00)00057-2
J. Bentsman, I. V. Dardynskaya, O. Shadyro, G. Pellegrinetti, R. Blauwkamp, G. Gloushonok
{"title":"Mathematical modeling and stochastic H∞ identification of the dynamics of the MF-influenced oxidation of hexane","authors":"J. Bentsman, I. V. Dardynskaya, O. Shadyro, G. Pellegrinetti, R. Blauwkamp, G. Gloushonok","doi":"10.1016/S0025-5564(00)00057-2","DOIUrl":"https://doi.org/10.1016/S0025-5564(00)00057-2","url":null,"abstract":"","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"118927434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-04-15DOI: 10.1016/S0025-5564(96)00171-X
Daniel Exelrod
{"title":"What is Life? The next fifty years. Speculations on the future of biology: Michael P. Murphy and Luke O'Neill, editors, Cambridge University Press, New York, USA, 1995, 202 pp., $24.95 (hardback)","authors":"Daniel Exelrod","doi":"10.1016/S0025-5564(96)00171-X","DOIUrl":"https://doi.org/10.1016/S0025-5564(96)00171-X","url":null,"abstract":"","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120265758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1996-03-01DOI: 10.1016/0025-5564(96)90013-9
B. Bell
{"title":"MLAB for DOS and MAC. Civilized Software, Inc., 7735 Old Georgetown Rd., Suite 410, Bethesda, Md 20814; (301)652-4741. $1,495 for the DOS version","authors":"B. Bell","doi":"10.1016/0025-5564(96)90013-9","DOIUrl":"https://doi.org/10.1016/0025-5564(96)90013-9","url":null,"abstract":"","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125721721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1995-05-01DOI: 10.1016/0025-5564(95)90051-9
L. Allen
{"title":"Modelling biological populations in space and time: Eric Renshaw, Cambridge Studies in Mathematical Biology, Cambridge Univ. Press, New York, 1993, 403 pp., $29.95 (paper back)","authors":"L. Allen","doi":"10.1016/0025-5564(95)90051-9","DOIUrl":"https://doi.org/10.1016/0025-5564(95)90051-9","url":null,"abstract":"","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128397568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1988-12-01DOI: 10.1016/0025-5564(88)90031-4
J. Jacquez, C. Simon, J. Koopman, L. Sattenspiel, T. Perry
{"title":"Modeling and analyzing HIV transmission: the effect of contact patterns","authors":"J. Jacquez, C. Simon, J. Koopman, L. Sattenspiel, T. Perry","doi":"10.1016/0025-5564(88)90031-4","DOIUrl":"https://doi.org/10.1016/0025-5564(88)90031-4","url":null,"abstract":"","PeriodicalId":383810,"journal":{"name":"Bellman Prize in Mathematical Biosciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126165668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：