{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:58:00Z","timestamp":1760144280637,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T00:00:00Z","timestamp":1711324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deputyship for Research and Innovation, Ministry of Education in Saudi Arabia","award":["ISP-2024"],"award-info":[{"award-number":["ISP-2024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper studies a nonlinear fractional mathematical model for hand, foot, and mouth Disease (HFMD), incorporating a vaccinated compartment. Our initial focus involves establishing the non-negativity and boundedness of the fractional order dynamical model. The existence and uniqueness of the system are discussed using the Caputo derivative operator formulation. Applying a fixed-point approach, we obtain results that confirm the presence of at least one solution. We analyze the stability behavior at the two equilibrium points (disease-free and endemic states) of the model and derive the basic reproduction number. Numerical simulations are conducted using the fractional Euler approach, and the simulation results confirm our analytical conclusions. This comprehensive approach enhances the understanding of HFMD dynamics and facilitates the policy making of health care centers to control the further spread of this disease.<\/jats:p>","DOI":"10.3390\/axioms13040213","type":"journal-article","created":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T12:32:36Z","timestamp":1711369956000},"page":"213","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7354-9107","authenticated-orcid":false,"given":"Aakash","family":"Mohandoss","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3843-5654","authenticated-orcid":false,"given":"Gunasundari","family":"Chandrasekar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering, Anna University, Chennai 600025, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9168-5126","authenticated-orcid":false,"given":"Mutum Zico","family":"Meetei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0186-0526","authenticated-orcid":false,"given":"Ahmed H.","family":"Msmali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"},{"name":"School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,25]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Turing instability of a Diffusive Predator-Prey Model along with an Allee Effect on a Predator","volume":"40","author":"Gunasundari","year":"2022","journal-title":"Commun. Math. Biol. 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