{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T13:08:39Z","timestamp":1771938519531,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T00:00:00Z","timestamp":1640304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["A1-S-45928"],"award-info":[{"award-number":["A1-S-45928"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0&lt;1. A similar result is obtained for the endemic equilibrium when R0&gt;1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge\u2013Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.<\/jats:p>","DOI":"10.3390\/axioms11010010","type":"journal-article","created":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T08:38:46Z","timestamp":1640335126000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1742-585X","authenticated-orcid":false,"given":"Nauman","family":"Ahmed","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Digital Technologies, Tallinn University, 10120 Tallinn, Estonia"},{"name":"Departamento de Mate\u1e3faticas y F\u00edsica, Universidad Aut\u0301onoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20130, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6443-9966","authenticated-orcid":false,"given":"Ali","family":"Raza","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Govt. Mulana Zafar Ali Khan Graduate College Wazirabad, Gujranwala 52250, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, 06530 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2165-3479","authenticated-orcid":false,"given":"Muhammad","family":"Rafiq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zafar","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Ozair","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Montoya, C., and Romero-Leiton, J.P. 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