{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T20:25:44Z","timestamp":1770409544537,"version":"3.49.0"},"reference-count":49,"publisher":"Informa UK Limited","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Population Studies"],"published-print":{"date-parts":[[1992,2]]},"DOI":"10.1080\/08898489209525339","type":"journal-article","created":{"date-parts":[[2009,9,21]],"date-time":"2009-09-21T06:30:35Z","timestamp":1253514635000},"page":"199-225","source":"Crossref","is-referenced-by-count":14,"title":["Empirical methods for the estimation of the mixing probabilities for socially structured populations from a single survey sample"],"prefix":"10.1080","volume":"3","author":[{"given":"Stephen P.","family":"Blythe","sequence":"first","affiliation":[{"name":"University of Strathctyde","place":["Scotland"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos","family":"Castillo\u2010Chavez","sequence":"additional","affiliation":[{"name":"Cornell University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George","family":"Casella","sequence":"additional","affiliation":[{"name":"Cornell University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","published-online":{"date-parts":[[2009,9,21]]},"reference":[{"key":"e_1_2_1_2_1","first-page":"241","article-title":"The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS","volume":"1","author":"Anderson R. M.","year":"1988","unstructured":"Anderson , R. M. 1988 . The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS . J. AIDS , 1 : 241 \u2013 256 .","journal-title":"J. AIDS"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1038\/333514a0"},{"key":"e_1_2_1_4_1","first-page":"417","article-title":"The significance of sexual partner contact networks for the transmission dynamics of HIV","volume":"3","author":"Anderson R. M.","year":"1990","unstructured":"Anderson , R. M. , Gupta , S. and Ng , W. 1990 . The significance of sexual partner contact networks for the transmission dynamics of HIV . J. of AIDS , 3 : 417 \u2013 429 .","journal-title":"J. of AIDS"},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1098\/rstb.1989.0074","article-title":"The transmission dynamics of the human immunodeficiency virus type 1 in the male homosexual community in the United Kingdom: the influence of changes in sexual behavior","volume":"325","author":"Anderson R. M.","year":"1989","unstructured":"Anderson , R. M. , Blythe , S. P. , Gupta , S. and Konnings , E. 1989 . The transmission dynamics of the human immunodeficiency virus type 1 in the male homosexual community in the United Kingdom: the influence of changes in sexual behavior . Phil Trans. R. Soc. London B , 325 : 45 \u2013 89 .","journal-title":"Phil Trans. R. Soc. London B"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1093\/imammb\/5.1.1"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/imammb\/5.3.181"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(89)90060-6"},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1038\/344202a0","article-title":"Scaling of sexual activity","volume":"344","author":"Blythe S. P.","year":"1990","unstructured":"Blythe , S. P. and Castillo\u2010Chavez , C. 1990a . Scaling of sexual activity . Nature , 344 : 202","journal-title":"Nature"},{"key":"e_1_2_1_10_1","article-title":"Towards a unified theory of mixing and pair\u2010formation","author":"Blythe S. P.","unstructured":"Blythe , S. P. , Castillo\u2010Chavez , C. , Palmer , J. S. and Cheng , M. A. in press . Towards a unified theory of mixing and pair\u2010formation . Math. Biosci. ,","journal-title":"Math. Biosci."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478599"},{"key":"e_1_2_1_12_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/978-3-642-93454-4_14","article-title":"Interaction, pair formation and force of infection terms in sexually transmitted diseases","volume":"83","author":"Busenberg S.","year":"1989","unstructured":"Busenberg , S. and Castillo\u2010Chavez , C. 1989 . Interaction, pair formation and force of infection terms in sexually transmitted diseases . Lea. Notes Biomath. , 83 : 289 \u2013 300 .","journal-title":"Lea. Notes Biomath."},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imammb\/8.1.1","article-title":"A general solution of the problem of mixing subpopulations, and its application to risk\u2010 and age\u2010structured epidemic models for the spread of AIDS","volume":"8","author":"Busenberg S.","year":"1991","unstructured":"Busenberg , S. and Castillo\u2010Chavez , C. 1991 . A general solution of the problem of mixing subpopulations, and its application to risk\u2010 and age\u2010structured epidemic models for the spread of AIDS . IMA J. of Mathematics Applied in Med and Biol. , 8 : 1 \u2013 29 .","journal-title":"IMA J. of Mathematics Applied in Med and Biol."},{"key":"e_1_2_1_14_1","series-title":"Lecture Notes in Biomathematics, No. 83","volume-title":"Mathematical and Statistical Approaches to AIDS Epidemiology","author":"Castillo\u2010Chavez C.","year":"1989","unstructured":"Castillo\u2010Chavez , C. 1989 . Mathematical and Statistical Approaches to AIDS Epidemiology , Lecture Notes in Biomathematics, No. 83 Edited by: Castillo\u2010Chavez , C. Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong : Springer Verlag ."},{"key":"e_1_2_1_15_1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/978-3-642-93454-4_13","article-title":"Mixing framework for social\/sexual behavior","volume":"83","author":"Castillo\u2010Chavez C.","year":"1989","unstructured":"Castillo\u2010Chavez , C. and Blythe , S. P. 1989 . Mixing framework for social\/sexual behavior . Lect. Notes Biomath. , 83 : 275 \u2013 284 .","journal-title":"Lect. Notes Biomath."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the International Conference on Differential Equations and Applications to Biology and Population Dynamics","author":"Castillo\u2010Chavez C.","unstructured":"Castillo\u2010Chavez , C. and Busenberg , S. On the solution of the two\u2010sex problem . Proceedings of the International Conference on Differential Equations and Applications to Biology and Population Dynamics . Edited by: Busenberg , S. and Martelli , M. Springer\u2010Verlag . Lecture Notes in Biomathematics, (in press)"},{"key":"e_1_2_1_17_1","first-page":"47","volume-title":"Differential Equations with Applications in Biology, Physics and Engineering","author":"Castillo\u2010Chavez C.","year":"1991","unstructured":"Castillo\u2010Chavez , C. , Busenberg , S. and Gerow , K. 1991 . \u201c Pair formation in structured populations \u201d . In Differential Equations with Applications in Biology, Physics and Engineering , Edited by: Goldstein , J. , Kappel , E and Schappacher , W. 47 \u2013 65 . New York : Marcel Dekker ."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00290636"},{"key":"e_1_2_1_19_1","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1007\/978-3-642-93454-4_9","article-title":"On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS) Part 2. Multiple group models","volume":"83","author":"Castillo\u2010Chavez C.","year":"1989","unstructured":"Castillo\u2010Chavez , C. , Cooke , K. , Huang , W. and Levin , S. A. 1989b . On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS) Part 2. Multiple group models . Lect. Notes Biomath. , 83 : 200 \u2013 217 .","journal-title":"Lect. Notes Biomath."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(89)90080-3"},{"key":"e_1_2_1_21_1","volume-title":"Proceedings SIMS conference on Statistical Methodology for the Study of the AIDS Epidemic","author":"Castillo\u2010Chavez C.","unstructured":"Castillo\u2010Chavez , C. , Shyu , S.\u2010F. , Rubin , G. and Umbach , D. On the estimation problem of mixing\/pair formation matrices with applications to models for sexually transmitted diseases . Proceedings SIMS conference on Statistical Methodology for the Study of the AIDS Epidemic . 1991 , Berkeley, CA. Boston : Birkhauser ."},{"key":"e_1_2_1_22_1","first-page":"303","volume-title":"Cross\u2010immunity in the dynamics of homogeneous and heterogeneous populations","author":"Castillo\u2010Chavez C.","unstructured":"Castillo\u2010Chavez , C. , Hethcote , H. W. , Andreasen , V , Levin , S. A. and Liu , W. M. Mathematical Ecology . Proceedings, Autumn Course Research Seminars . Cross\u2010immunity in the dynamics of homogeneous and heterogeneous populations , Edited by: Gross , L. , Hal\u2010lam , T. G. and Levin , S. A. pp. 303 \u2013 316 . Singapore : World Scientific Publishing Co. . Trieste 1986"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00290636"},{"key":"e_1_2_1_24_1","first-page":"297","volume-title":"Proceedings of the 2nd International Conference on Differential Equations and its Applications","author":"Cooke K. L.","unstructured":"Cooke , K. L. , Allers , D. A. and Castillo\u2010Chavez , G . Mixing patterns models of AIDS . Proceedings of the 2nd International Conference on Differential Equations and its Applications . Edited by: Arino , Ovide , Axelro , D. and Kimmel , M. pp. 297 \u2013 309 . Rutgers 1989"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1989.0078"},{"key":"e_1_2_1_26_1","series-title":"Report BU\u20101105\u2010M","volume-title":"A methodology for asking sensitive questions among college undergraduates. Biometrics Unit Itch","author":"Crawford C. M.","year":"1990","unstructured":"Crawford , C. M. , Schwager , S. J. and Castillo\u2010Chavez , C. 1990 . A methodology for asking sensitive questions among college undergraduates. Biometrics Unit Itch , Report BU\u20101105\u2010M Ithaca, NY : Cornell University ."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1989.0077"},{"issue":"6","key":"e_1_2_1_28_1","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1086\/284827","article-title":"Processes of pair formation leading to assortative mating in biological populations: encounter mating model","volume":"131","author":"Gimelfarb A.","year":"1988","unstructured":"Gimelfarb , A. 1988a . Processes of pair formation leading to assortative mating in biological populations: encounter mating model . Amer. Natur. , 131 (6) : 865 \u2013 884 .","journal-title":"Amer. Natur."},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-5809(88)90032-9"},{"key":"e_1_2_1_30_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1097\/00002030-198912000-00005","article-title":"Network of sexual contacts: implications for the pattern of spread of HIV","volume":"3","author":"Gupta S.","year":"1989","unstructured":"Gupta , S. , Anderson , R. M. and May , R. M. 1989 . Network of sexual contacts: implications for the pattern of spread of HIV . AIDS , 3 : 1 \u2013 11 .","journal-title":"AIDS"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07544-9"},{"key":"e_1_2_1_32_1","unstructured":"Hethcote H. W. Ven Ark J. W. Karon J. M. and Longini Jr. I. M. A simulation of HIV and AIDS in homosexual men in San Francisco. Unpublished manuscript."},{"key":"e_1_2_1_33_1","volume-title":"Studies in Differential Equations and Applications","author":"Huang W.","year":"1989","unstructured":"Huang , W. 1989 . Studies in Differential Equations and Applications , Claremont, CA : The Claremont Graduate School . Ph.D. dissertation"},{"key":"e_1_2_1_34_1","article-title":"Stability and befurcation for a multiple group model for the dynamics of HIV\/AIDS transmission","author":"Huang W.","year":"1991","unstructured":"Huang , W. , Cooke , K. and Castillo\u2010Chavez , C. 1991 . Stability and befurcation for a multiple group model for the dynamics of HIV\/AIDS transmission . SIAMJ. of Applied Math , (accepted)","journal-title":"SIAMJ. of Applied Math"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1989.0076"},{"key":"e_1_2_1_36_1","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0025-5564(88)90031-4","article-title":"Modeling and analyzing HIV transmission: the effects of contact patterns","volume":"92","author":"Jacquez J. A.","year":"1989","unstructured":"Jacquez , J. A. , Simon , C. P. , Koopman , J. , Sattenspiel , L. and Perry , T. 1989 . Modeling and analyzing HIV transmission: the effects of contact patterns . Math. Bios. , 92 : 119 \u2013 199 .","journal-title":"Math. Bios."},{"key":"e_1_2_1_37_1","first-page":"542","article-title":"The projected incidence of AIDS and estimated prevalence of HIV infection in the United States","volume":"1","author":"Karon J. M.","year":"1988","unstructured":"Karon , J. M. , Dondero , T. J. and Curran , J. W. 1988 . The projected incidence of AIDS and estimated prevalence of HIV infection in the United States . J. of AIDS , 1 : 542 \u2013 550 .","journal-title":"J. of AIDS"},{"key":"e_1_2_1_38_1","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/978-3-642-93454-4_3","article-title":"Predicting AIDS incidence by extrapolating from recent trends","volume":"83","author":"Karon J. M.","year":"1989","unstructured":"Karon , J. M. , Dondero , T. J. and Cunan , J. W. 1989 . Predicting AIDS incidence by extrapolating from recent trends . Lect Notes Biomath. , 83 : 58 \u2013 88 .","journal-title":"Lect Notes Biomath."},{"key":"e_1_2_1_39_1","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1007\/978-3-642-46693-9_19","article-title":"Small models are beautiful: Efficient estimators are even more beautiful","volume":"81","author":"Ludwig D.","year":"1989","unstructured":"Ludwig , D. 1989 . Small models are beautiful: Efficient estimators are even more beautiful . Lect. Notes Biomath. , 81 : 274 \u2013 281 .","journal-title":"Lect. Notes Biomath."},{"key":"e_1_2_1_40_1","first-page":"559","article-title":"Are age structured models appropriate for catch\u2010effort data?","volume":"40","author":"Ludwig D.","year":"1985","unstructured":"Ludwig , D. and Walters , C. 1985 . Are age structured models appropriate for catch\u2010effort data? . Can. J. Fish. Aquat. Sci. , 40 : 559 \u2013 569 .","journal-title":"Can. J. Fish. Aquat. Sci."},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(80)90069-3"},{"key":"e_1_2_1_42_1","series-title":"Biometrics Unit Technical Report (BU\u20101122\u2010M)","volume-title":"State\u2010dependent mixing and state\u2010dependent contact rates in epidemiological models","author":"Palmer J. S.","year":"1991","unstructured":"Palmer , J. S. , Castillo\u2010Chavez , C. and Blythe , S. P. 1991 . State\u2010dependent mixing and state\u2010dependent contact rates in epidemiological models , Biometrics Unit Technical Report (BU\u20101122\u2010M)"},{"key":"e_1_2_1_43_1","series-title":"Biometrics Unit Tech. Report BU\u20101112\u2010M","volume-title":"Application of capture\u2010recapture methodology to estimation of size of population at risk of AIDS and\/or other sexually\u2010transmitted diseases","author":"Rubin G.","year":"1991","unstructured":"Rubin , G. , Umbauch , D. , Shyu , S\u2010F. and Castillo\u2010Chavez , C. 1991 . Application of capture\u2010recapture methodology to estimation of size of population at risk of AIDS and\/or other sexually\u2010transmitted diseases , Biometrics Unit Tech. Report BU\u20101112\u2010M Ithaca, New York : Cornell University ."},{"key":"e_1_2_1_44_1","first-page":"411","article-title":"Population structure and the spread of disease","volume":"59","author":"Sattenspiel L.","year":"1987","unstructured":"Sattenspiel , L. 1987a . Population structure and the spread of disease . Human Biology , 59 : 411 \u2013 438 .","journal-title":"Human Biology"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1002\/ajpa.1330730212"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1002\/ajhb.1310020408"},{"key":"e_1_2_1_47_1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/978-3-642-93454-4_1","article-title":"Statistical and mathematical approaches in HIV\/AIDS modelling: A review","volume":"83","author":"Schwager S. J.","year":"1989","unstructured":"Schwager , S. J. , Castillo\u2010Chavez , C. and Hethcote , H. 1989 . Statistical and mathematical approaches in HIV\/AIDS modelling: A review . Lect. Notes Biomath. , 83 : 2 \u2013 35 .","journal-title":"Lect. Notes Biomath."},{"key":"e_1_2_1_48_1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/978-3-642-93454-4_7","article-title":"On the role of variable infectivity in the dynamics of the human immunodeficiency virus","volume":"83","author":"Thieme H. R.","year":"1989","unstructured":"Thieme , H. R. and Castillo\u2010Chavez , C. 1989 . On the role of variable infectivity in the dynamics of the human immunodeficiency virus . Lect Notes Biomath. , 83 : 157 \u2013 176 .","journal-title":"Lect Notes Biomath."},{"key":"e_1_2_1_49_1","series-title":"Biometrics Unit Tech. Report BU\u20101102\u2010M","volume-title":"How May Infection\u2010Age Dependent Infectivity Affect the Dynamics of HIV\/AIDS","author":"Thieme H. R.","year":"1991","unstructured":"Thieme , H. R. and Castillo\u2010Chavez , C. 1991 . How May Infection\u2010Age Dependent Infectivity Affect the Dynamics of HIV\/AIDS , Biometrics Unit Tech. Report BU\u20101102\u2010M Ithaca, NY : Cornell University ."},{"key":"e_1_2_1_50_1","unstructured":"To whom all correspondence should be addressed."}],"container-title":["Mathematical Population Studies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/08898489209525339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T09:50:32Z","timestamp":1770371432000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/08898489209525339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,2]]},"references-count":49,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,2]]}},"alternative-id":["10.1080\/08898489209525339"],"URL":"https:\/\/doi.org\/10.1080\/08898489209525339","relation":{},"ISSN":["0889-8480","1547-724X"],"issn-type":[{"value":"0889-8480","type":"print"},{"value":"1547-724X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,2]]}}}