{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:12:37Z","timestamp":1787029957893,"version":"build-2736575974"},"reference-count":72,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["R.G.P.2\/207\/43"],"award-info":[{"award-number":["R.G.P.2\/207\/43"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we present a new general solution to a rational epidemiological mathematical model via a recent intelligent method called the natural transform homotopy analysis method (NTHAM), which combines two methods: the natural transform method (NTM) and homotopy analysis method (HAM). To assess the precision and the reliability of the present method, we compared the obtained results with those of the Laplace homotopy perturbation method (LHPM) as well as the q-homotopy analysis Sumudu transform method (q-HASTM), which revealed that the NTHAM is more reliable. The Caputo fractional derivative is employed. It not only gives initial conditions with obvious natural interpretation but is also bounded, meaning that there is no derivative of a constant. The results show that the proposed technique is superior in terms of simplicity, quality, accuracy, and stability and demonstrate the effectiveness of the rational technique under consideration.<\/jats:p>","DOI":"10.3390\/sym14081695","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T23:44:03Z","timestamp":1660607043000},"page":"1695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Analytical Study of Fractional Epidemic Model via Natural Transform Homotopy Analysis Method"],"prefix":"10.3390","volume":"14","author":[{"given":"Hamdy R.","family":"Abdl-Rahim","sequence":"first","affiliation":[{"name":"Industrial Technical Institute, Medium Valley Technological College, Ministry of Higher Education, Sohag 82786, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3305-7340","authenticated-orcid":false,"given":"Mohra","family":"Zayed","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9060-4371","authenticated-orcid":false,"given":"Gamal M.","family":"Ismail","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt"},{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"ref_1","unstructured":"Breuer, F., and Driesch, V.D. 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