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A."],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:p>\n                    This paper is concerned primarily with constructive mathematical analysis of a general system of nonlinear two-point boundary value problem when an empirically constructed candidate for an approximate solution (\n                    <jats:italic>quasi-solution<\/jats:italic>\n                    ) satisfies verifiable conditions. A local analysis in a neighbour- hood of a\n                    <jats:italic>quasi-solution<\/jats:italic>\n                    assures the existence and uniqueness of solutions and, at the same time, provides error bounds for approximate solutions. Applying this method to a cholera epidemic model, we obtain an analytical approximation of the steady-state solution with rigorous error bounds that also displays dependence on a parameter. In connection with this epidemic model, we also analyse the basic reproduction number, an important threshold quantity in the epidemiology context. Through a complex analytic approach, we determine the principal eigenvalue to be real and positive in a range of parameter values.\n                  <\/jats:p>","DOI":"10.1098\/rspa.2019.0673","type":"journal-article","created":{"date-parts":[[2020,2,25]],"date-time":"2020-02-25T19:06:13Z","timestamp":1582657573000},"page":"20190673","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonlinear two-point boundary value problems: applications to a cholera epidemic model"],"prefix":"10.1098","volume":"476","author":[{"given":"Atiqur","family":"Chowdhury","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88001, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3959-7660","authenticated-orcid":true,"given":"Saleh","family":"Tanveer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ohio State University, Columbus, OH 43210, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6445-8887","authenticated-orcid":true,"given":"Xueying","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2020,2,26]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-010-0309-7"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002080010010"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/S111111110240176X"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-002-0080-8"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/16M1073789"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-006-0003-y"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/25\/1\/125"},{"key":"e_1_3_8_9_2","doi-asserted-by":"publisher","DOI":"10.1215\/00127094-2429589"},{"key":"e_1_3_8_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-016-2588-9"},{"key":"e_1_3_8_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2018.08.039"},{"key":"e_1_3_8_12_2","volume-title":"Reaction-diffusion equations and their applications to biology","author":"Britton NF","year":"1986"},{"key":"e_1_3_8_13_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2008.21.1"},{"key":"e_1_3_8_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.021907"},{"key":"e_1_3_8_15_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1179047"},{"key":"e_1_3_8_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.04.006"},{"key":"e_1_3_8_17_2","volume-title":"Mathematical epidemiology of infectious diseases: model building, analysis and interpretation","author":"Diekmann O","year":"2000"},{"key":"e_1_3_8_18_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2005.0042"},{"key":"e_1_3_8_19_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198545996.001.0001","volume-title":"Infectious diseases of humans: dynamics and control","author":"Anderson RM","year":"1991"},{"key":"e_1_3_8_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00178324"},{"key":"e_1_3_8_21_2","doi-asserted-by":"publisher","DOI":"10.1137\/13091470X"},{"key":"e_1_3_8_22_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016073"},{"key":"e_1_3_8_23_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016.21.1297"},{"key":"e_1_3_8_24_2","first-page":"559","article-title":"Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model","volume":"14","author":"Yamazaki K","year":"2017","journal-title":"Math. 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