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The mathematical model categorizes the breathing transmission epidemic model into four dynamics based on a nonlinear stiff ordinary differential system: susceptible, exposed, infected, and recovered. Three different cases of the model are taken and numerically presented by applying the stochastic SCGGNNs. An activation function \u2018log-sigmoid\u2019 uses twenty neurons in the hidden layers. The precision of SCGGNNs is obtained by comparing the proposed and database solutions. While the negligible absolute error is performed around 10<jats:sup>\u201306<\/jats:sup> to 10<jats:sup>\u201307<\/jats:sup>, it enhances the accuracy of the scheme. The obtained results of the breathing transmission epidemic system have been provided using the training, verification, and testing procedures to reduce the mean square error. Moreover, the exactness and capability of the stochastic SCGGNNs are approved through error histograms, regression values, correlation tests, and state transitions.<\/jats:p>","DOI":"10.1038\/s41598-023-43324-2","type":"journal-article","created":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T11:02:24Z","timestamp":1695812544000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A computational stochastic procedure for solving the epidemic breathing transmission system"],"prefix":"10.1038","volume":"13","author":[{"given":"Najah","family":"AbuAli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Bilal","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zulqurnain","family":"Sabir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,27]]},"reference":[{"key":"43324_CR1","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.ijregi.2022.01.011","volume":"2","author":"A Mahdi","year":"2022","unstructured":"Mahdi, A. et al. 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