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Our results indicate that environmental pollution and bacterial hyper-infectivity can increase the chance of epidemic spreading.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/nhm.2024042","type":"journal-article","created":{"date-parts":[[2024,9,25]],"date-time":"2024-09-25T10:41:43Z","timestamp":1727260903000},"page":"940-969","source":"Crossref","is-referenced-by-count":0,"title":["Influence of environmental pollution and bacterial hyper-infectivity on dynamics of a waterborne pathogen model with free boundaries"],"prefix":"10.3934","volume":"19","author":[{"given":"Meng","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"},{"name":"Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiancheng","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"},{"name":"Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yindi","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2024042-1","doi-asserted-by":"publisher","unstructured":"J. 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