{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T16:41:54Z","timestamp":1769186514735,"version":"3.49.0"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"vor","delay-in-days":271,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP.2\/116\/43"],"award-info":[{"award-number":["RGP.2\/116\/43"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>Whooping cough is a highly transmitted disease around the world. According to the World Health Organization (WHO), 0.15 million cases had reported globally in 2018. Most of the Asian and African states are infected regions. Through the study, we investigated the whole population into the four classes susceptible (S), exposed (E), infected (I), and vaccinated or recovered (R). The transmission dynamics of whooping cough disease are studied analytically and numerically. Analytical analyses are positivity, boundedness, reproduction number, equilibria, and local and global stabilities. In numerical analysis, we developed an implicit numerical integration scheme consistent with the biological problem\u2019s properties. The analysis of the implicit method for the said model is dynamically consistent, positive, and bounded. Furthermore, an implicit numerical integration scheme is suitable for studying a particular epidemic model such as the whooping cough disease.<\/jats:p>","DOI":"10.1155\/2022\/3642444","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T18:05:15Z","timestamp":1664474715000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A SEIR Epidemic Model of Whooping Cough\u2010Like Infections and Its Dynamically Consistent Approximation"],"prefix":"10.1155","volume":"2022","author":[{"given":"M.M.","family":"Alqarni","sequence":"first","affiliation":[]},{"given":"Arooj","family":"Nasir","sequence":"additional","affiliation":[]},{"given":"Maryam Ahmed","family":"Alyami","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6443-9966","authenticated-orcid":false,"given":"Ali","family":"Raza","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Awrejcewicz","sequence":"additional","affiliation":[]},{"given":"Muhammad","family":"Rafiq","sequence":"additional","affiliation":[]},{"given":"Nauman","family":"Ahmed","sequence":"additional","affiliation":[]},{"given":"Tahira","family":"Sumbal Shaikh","sequence":"additional","affiliation":[]},{"given":"Emad E.","family":"Mahmoud","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"e_1_2_7_1_2","article-title":"A Network-Based compartmental model for the spread of whooping cough in Nebraska","volume":"388","author":"Ameri K.","year":"2019","journal-title":"AMIA Summits on Translational Science Proceedings"},{"key":"e_1_2_7_2_2","first-page":"79","article-title":"Numerical analysis of a modified SIR epidemic model with the effect of time delay","volume":"51","author":"Ali M. 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