{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T03:10:01Z","timestamp":1792293001962,"version":"4.4.0"},"reference-count":43,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,2,28]],"date-time":"2006-02-28T00:00:00Z","timestamp":1141084800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Risk Analysis"],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p>The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose\u2010response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence\u2010based approaches. However, the method uses knowledge of the conditional dose\u2010response form, and this form is not well established for the illness endpoint. A conditional parametric dose\u2010response function for gastroenteric illness is proposed here based on simple numerical models of self\u2010organized host\u2010pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self\u2010organized critical value of wellness. A generalized beta\u2010Poisson illness dose\u2010response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose\u2010response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 \u00d7 10<jats:sup>\u22127<\/jats:sup>oocysts\/exposure (e.g., 2.5 \u00d7 10<jats:sup>\u22127<\/jats:sup>oocysts\/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson\u2010distributed pathogen counts. This estimate should be revised to account for non\u2010Poisson distributions of<jats:italic>Cryptosporidium parvum<\/jats:italic>in drinking water and total response, considering secondary illness propagation in the population.<\/jats:p>","DOI":"10.1111\/j.1539-6924.2006.00745.x","type":"journal-article","created":{"date-parts":[[2006,2,28]],"date-time":"2006-02-28T20:23:56Z","timestamp":1141158236000},"page":"543-554","source":"Crossref","is-referenced-by-count":20,"title":["Predictive Bayesian Microbial Dose\u2010Response Assessment Based on Suggested Self\u2010Organization in Primary Illness Response:<i>Cryptosporidium parvum<\/i>"],"prefix":"10.1111","volume":"26","author":[{"given":"James D.","family":"Englehardt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeff","family":"Swartout","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,2,28]]},"reference":[{"key":"e_1_2_8_2_1","first-page":"504","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz M.","year":"1972"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.59.381"},{"key":"e_1_2_8_4_1","first-page":"684","volume-title":"Probability, Statistics, and Decision for Civil Engineers","author":"Benjamin J.","year":"1970"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/clinids\/10.1.111"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.4269\/ajtmh.1999.60.157"},{"key":"e_1_2_8_7_1","unstructured":"Chow V.(1954).The log\u2010probability law and its engineering applications.Proceedings of the American Society of Civil Engineers 80(536) 1\u201325."},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM199503303321304"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.286.5446.1882"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9372(1995)121:6(455)"},{"key":"e_1_2_8_11_1","unstructured":"Englehardt J.(2001).Predictive Bayesian microbial dose\u2010response functions for mutually adaptive populations.Presentation Society for Risk Analysis Annual Meeting Seattle December 2\u20135 Society for Risk Analysis McLean VA ."},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/0272-4332.00016"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/10807030490280963"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/15287390490428080"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0042-6822(67)90271-1"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0043-1354(01)00350-5"},{"issue":"3","key":"e_1_2_8_17_1","first-page":"117","article-title":"Drinking water treatment increases micro\u2010organism clustering: The implications for microbiological risk assessment","volume":"46","author":"Gale P.","year":"1997","journal-title":"Journal of Water Supply Research and Technology\u2014Aqua"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4485-6"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0950268800050366"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1551-8833.1996.tb06619.x"},{"key":"e_1_2_8_21_1","first-page":"449","volume-title":"Quantitative Microbial Risk Assessment","author":"Haas C.","year":"1999"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1286-4579(99)80005-7"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-1951(64)90016-2"},{"key":"e_1_2_8_24_1","first-page":"13","volume-title":"Essentials of Infectious Diseases","author":"Mandell L.","year":"1985"},{"key":"e_1_2_8_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-1605(96)00994-4"},{"key":"e_1_2_8_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0043-1354(01)00119-1"},{"key":"e_1_2_8_27_1","first-page":"414","volume-title":"Mims' Pathogenesis of Infectious Disease","author":"Mims C.","year":"1995"},{"key":"e_1_2_8_28_1","doi-asserted-by":"publisher","DOI":"10.1086\/315033"},{"key":"e_1_2_8_29_1","doi-asserted-by":"publisher","DOI":"10.1086\/340132"},{"key":"e_1_2_8_30_1","volume-title":"Theoretical Immunology: Parts One & Two","author":"Perelson A.","year":"1992"},{"key":"e_1_2_8_31_1","first-page":"7","volume-title":"Clinical Infectious Diseases: A Practical Approach","author":"Root R.","year":"1999"},{"key":"e_1_2_8_32_1","volume-title":"The Mathematical Theory of Communication","author":"Shannon C. 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