{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:30:28Z","timestamp":1787225428043,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740858"],"award-info":[{"award-number":["CCF-1740858"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2028401"],"award-info":[{"award-number":["DMS-2028401"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2022,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic Susceptible, Infected, Recovered (SIR) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona.<\/jats:p>","DOI":"10.1137\/21m1450719","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T13:38:20Z","timestamp":1671111500000},"page":"2036-2056","source":"Crossref","is-referenced-by-count":0,"title":["Epidemics from the Eye of the Pathogen"],"prefix":"10.1137","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2521-4331","authenticated-orcid":true,"given":"Faryad D.","family":"Sahneh","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Arizona, Tucson, AZ 85721 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9591-2162","authenticated-orcid":true,"given":"William","family":"Fries","sequence":"additional","affiliation":[{"name":"Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6464-1972","authenticated-orcid":true,"given":"Joseph C.","family":"Watkins","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Interdisciplinary Program in Applied Mathematics, Department of Epidemiology and Biostatistics, BIO5 Institute, University of Arizona, Tucson, AZ 85721 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2064-229X","authenticated-orcid":true,"given":"Joceline","family":"Lega","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Department of Epidemiology and Biostatistics, BIO5 Institute, University of Arizona, Tucson, AZ 85721 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,12,16]]},"reference":[{"key":"ref1","unstructured":"The COVID Tracking Project at The Atlantic, https:\/\/covidtracking.com\/data\/api (6 January 2021) (All data and content are available under a CC BY 4.0 license, https:\/\/covidtracking.com\/license)."},{"key":"ref2","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.2517-6161.1949.tb00031.x","volume":"11","author":"Bartlett M.","year":"1949","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"key":"ref3","series-title":"Addison-Wesley Ser. Statist.","volume-title":"Probability","author":"Breiman L.","year":"1968"},{"key":"ref4","volume":"6","author":"Chowell G.","year":"2014","journal-title":"PLoS Curr."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1038\/s43588-021-00028-9"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316658"},{"key":"ref7","first-page":"1309","volume":"20","author":"Ghosh M.","year":"2010","journal-title":"Statist. Sinica"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(76)90041-3"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-01121-y"},{"key":"ref10","first-page":"700","volume":"115","author":"Kermack W. O.","year":"1927","journal-title":"Proc. A"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2021.1912419"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.epidem.2016.10.002"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1371\/journal.ppat.1003467"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-40413-4_10"},{"key":"ref15","unstructured":"B. Rudis , cdcfluview: Retrieve Flu Season Data from the United States Centers for Disease Control and Prevention (CDC) \u201cFluView\u201d Portal, 2020, R package version 0.9.2., https:\/\/CRAN.R-project.org\/package=cdcfluview."},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.2307\/1427116"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-10067-7_18"},{"key":"ref18","unstructured":"State of Arizona, Executive Order 2020-33, Returning Stronger. Amending the Stay Home, Stay Healthy, Stay Connected Order, https:\/\/azgovernor.gov\/executive-orders (April 29, 2020)."},{"key":"ref19","unstructured":"State of Arizona, Executive Order 2020-09, Limiting the Operations of Certain Businesses to Slow the Spread of COVID-19, https:\/\/azgovernor.gov\/executive-orders (March 19, 2020)."},{"key":"ref20","unstructured":"State of Arizona, Executive Order 2020-18, Stay Home, Stay Healthy, https:\/\/azgovernor.gov\/executive-orders."},{"key":"ref21","author":"State of Arizona","journal-title":"Executive Order 2020-36, Stay Healthy, Return Smarter, Return Stronger"},{"key":"ref22","unstructured":"State of Arizona, Executive Order 2020-34, Building on COVID-19 Successes, https:\/\/azgovernor.gov\/executive-orders (May 4, 2020)."},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.epidem.2018.05.007"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1450719","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:12:18Z","timestamp":1787224338000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1450719"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,16]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,12,31]]}},"alternative-id":["10.1137\/21M1450719"],"URL":"https:\/\/doi.org\/10.1137\/21m1450719","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,16]]}}}