{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T19:21:29Z","timestamp":1778700089395,"version":"3.51.4"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"National Science Foundation","award":["DMS-1446139"],"award-info":[{"award-number":["DMS-1446139"]}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["U54CA132383"],"award-info":[{"award-number":["U54CA132383"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stoch. Dyn."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:p> Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of It\u00f4 stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value [Formula: see text] is defined in terms of the basic reproduction number [Formula: see text] for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When [Formula: see text], the cholera infection will extinct within finite periods of time almost surely. When [Formula: see text], the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number [Formula: see text] for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that [Formula: see text], the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out. <\/jats:p>","DOI":"10.1142\/s0219493721500118","type":"journal-article","created":{"date-parts":[[2020,6,6]],"date-time":"2020-06-06T13:44:15Z","timestamp":1591451055000},"page":"2150011","source":"Crossref","is-referenced-by-count":17,"title":["Dynamics of cholera epidemic models in fluctuating environments"],"prefix":"10.1142","volume":"21","author":[{"given":"Tuan Anh","family":"Phan","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, New Mexico State University, 1290 Frenger Mall, MSC 3MB\/Science Hall 236, Las Cruces, New Mexico 88003 8001, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2292-213X","authenticated-orcid":false,"given":"Jianjun Paul","family":"Tian","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, New Mexico State University, 1290 Frenger Mall, MSC 3MB\/Science Hall 236, Las Cruces, New Mexico 88003 8001, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bixiang","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, New Mexico Institute of Mining and Technology, 801 Leroy Pl, Socorro, NM 87801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,6,5]]},"reference":[{"key":"S0219493721500118BIB001","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold L.","year":"1972"},{"key":"S0219493721500118BIB002","doi-asserted-by":"crossref","first-page":"051901-1","DOI":"10.1103\/PhysRevE.81.051901","volume":"81","author":"Azaele S.","year":"2010","journal-title":"Phys. Rev. E"},{"key":"S0219493721500118BIB003","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1186\/s13662-017-1406-9","volume":"2017","author":"Bao K.","year":"2017","journal-title":"Adv. Differential Equations"},{"key":"S0219493721500118BIB004","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1007\/s00477-014-0906-3","volume":"30","author":"Bertuzzo E.","year":"2016","journal-title":"Stoch. Environ. Res. Assess."},{"key":"S0219493721500118BIB005","first-page":"121","volume":"27","author":"Capasso V.","year":"1979","journal-title":"Revue depid\u00e9moligi\u00e9 sant\u00e9 Publ."},{"key":"S0219493721500118BIB007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2334-1-1","volume":"1","author":"Codeco C. T.","year":"2001","journal-title":"BMC Infect. Dis."},{"key":"S0219493721500118BIB008","first-page":"234","volume":"51","author":"Gain J.","year":"2009","journal-title":"Austral. New Zealand Indust. Appl. Math. J."},{"key":"S0219493721500118BIB009","volume-title":"Introduction to Stochastic Differential Equations","author":"Gard T. C.","year":"1988"},{"key":"S0219493721500118BIB010","doi-asserted-by":"crossref","first-page":"0063","DOI":"10.1371\/journal.pmed.0030063","volume":"3","author":"Hartley D. M.","year":"2006","journal-title":"PLoS Medicine"},{"key":"S0219493721500118BIB011","doi-asserted-by":"crossref","first-page":"4652","DOI":"10.1073\/pnas.0600166103","volume":"103","author":"Jensen M.","year":"2006","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"S0219493721500118BIB012","series-title":"Stochastic Modeling and Applied Probability","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-23280-0","volume-title":"Stochastic Stability of Differential Equations","volume":"66","author":"Khasminskii R.","year":"2012","edition":"2"},{"key":"S0219493721500118BIB013","volume-title":"Numerical Solution of Stochastic Differential Equations","author":"Kloeden P. E.","year":"1995"},{"key":"S0219493721500118BIB014","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1016\/j.spl.2012.12.021","volume":"83","author":"Lahrouz A.","year":"2013","journal-title":"Stat. Probab. Lett."},{"key":"S0219493721500118BIB015","doi-asserted-by":"crossref","first-page":"59","DOI":"10.15388\/NA.16.1.14115","volume":"16","author":"Lahrouz A.","year":"2011","journal-title":"Nonlinear Anal. Model. Control"},{"key":"S0219493721500118BIB016","volume-title":"Stochastic Differential Equations and Applications","author":"Mao X.","year":"2007","edition":"2"},{"key":"S0219493721500118BIB017","doi-asserted-by":"crossref","DOI":"10.1515\/9780691206912","volume-title":"Stability and Complexity in Model Ecosystems","author":"May R. M.","year":"2001"},{"key":"S0219493721500118BIB018","doi-asserted-by":"crossref","first-page":"8767","DOI":"10.1073\/pnas.1019712108","volume":"108","author":"Mukandavire Z.","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"S0219493721500118BIB019","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1186\/s12976-017-0061-x","volume":"14","author":"Nishiura H.","year":"2017","journal-title":"Theoret. Biol. Med. Model."},{"key":"S0219493721500118BIB020","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1371\/journal.pmed.0030280","volume":"3","author":"Pascual M.","year":"2006","journal-title":"PLoS Medicine"},{"key":"S0219493721500118BIB021","volume-title":"Linear Algebra and Its Applications","author":"Strang G.","year":"1988"},{"key":"S0219493721500118BIB023","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.mbs.2011.04.001","volume":"232","author":"Tian J. P.","year":"2011","journal-title":"Math. Biosci."},{"key":"S0219493721500118BIB025","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.jmaa.2011.11.072","volume":"388","author":"Yang Q.","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"S0219493721500118BIB026","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1137\/060649343","volume":"46","author":"Zhu C.","year":"2007","journal-title":"SIAM J. Control Optim."}],"container-title":["Stochastics and Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219493721500118","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T05:57:40Z","timestamp":1609221460000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219493721500118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,5]]},"references-count":23,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1142\/S0219493721500118"],"URL":"https:\/\/doi.org\/10.1142\/s0219493721500118","relation":{},"ISSN":["0219-4937","1793-6799"],"issn-type":[{"value":"0219-4937","type":"print"},{"value":"1793-6799","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,5]]}}}