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Due to lack of substantial knowledge about the virus diffusion and the effect of external perturbations, the model is extended to the probabilistic formulation with L\u00e9vy jumps. The proposed model is a two block compartmental system that requires the form of It\u00f4-L\u00e9vy stochastic differential equations. Based on some assumptions and nonstandard analytical techniques, two principal asymptotic properties are proved: the eradication and continuation in the mean of <italic>Monkeypox<\/italic> 2022. The outcomes of the study reveals that the dynamical behavior of the proposed <italic>Monkeypox<\/italic> 2022 system is chiefly governed by some parameters that are precisely correlated with the noise intensities. To support the obtained theoretical finding, examples based on numerical simulations and real data are presented at the end of the study. The numerical simulations also exhibit the impact of the innovative adopted mathematical techniques on the findings of this work.<\/p><\/abstract><\/jats:p>","DOI":"10.3934\/mbe.2022633","type":"journal-article","created":{"date-parts":[[2022,9,15]],"date-time":"2022-09-15T11:00:04Z","timestamp":1663239604000},"page":"13560-13581","source":"Crossref","is-referenced-by-count":54,"title":["Stochastic modeling of the <i>Monkeypox<\/i> 2022 epidemic with cross-infection hypothesis in a highly disturbed environment"],"prefix":"10.3934","volume":"19","author":[{"given":"Asad","family":"Khan","sequence":"first","affiliation":[{"name":"School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yassine","family":"Sabbar","sequence":"additional","affiliation":[{"name":"LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anwarud","family":"Din","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2022633-1","unstructured":"WHO, Monkeypox, 2022. 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