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The local asymptotic stability of the disease-free equilibrium point is examined through sensitivity and qualitative analyses, particularly using the basic reproduction number, <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$ R_0 $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>R<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. The proposed scheme is rigorously validated through fixed point theory, ensuring the model is evidence-based. A case study conducted in Saudi Arabia demonstrates the effectiveness of the proposed model, yielding successful verification through real-world numerical analysis. The results indicate that incorporating fractional derivatives leads to a more robust model, particularly in assessing the long-term impact of vaccination on the COVID-19 epidemic. The findings underscore the significant role of vaccination in reducing <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$ R_0 $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>R<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and achieving a disease-free state. This work highlights the potential of fractional operators in epidemiological modeling, providing crucial insights into strategies for preventing the transmission of COVID-19 and similar diseases.<\/jats:p>","DOI":"10.1007\/s12190-024-02357-0","type":"journal-article","created":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T07:54:43Z","timestamp":1736322883000},"page":"3233-3254","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Ulam-hyres stability analysis and fractional operator implications on the Covid-19 virus dynamics with long-term vaccination effects"],"prefix":"10.1007","volume":"71","author":[{"given":"Muhammad","family":"Farman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saba","family":"Jamil","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Evren","family":"Hincal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aceng","family":"Sambas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,1,8]]},"reference":[{"issue":"772","key":"2357_CR1","first-page":"700","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. 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