{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:32:01Z","timestamp":1760149921878,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,23]],"date-time":"2023-09-23T00:00:00Z","timestamp":1695427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371494","11971279","12231012","202202020101010"],"award-info":[{"award-number":["12371494","11971279","12231012","202202020101010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013317","name":"Shanxi Provincial Key Research and Development Project","doi-asserted-by":"publisher","award":["12371494","11971279","12231012","202202020101010"],"award-info":[{"award-number":["12371494","11971279","12231012","202202020101010"]}],"id":[{"id":"10.13039\/501100013317","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Mathematical modeling in epidemiology, biology, and life sciences requires the use of stochastic models. In this paper, we derive a competitive two-strain stochastic SIR epidemic model by considering the change in state of the epidemic process due to an event. Based on the density-dependent process theory, we construct a six-dimensional deterministic model that can be used to describe the diffusion limit of the stochastic epidemic on a heterogeneous network. Furthermore, we show the explicit expressions for the variances of infectious individuals with strain 1 and strain 2 when the level of infection is increasing exponentially. In particular, we find that the expressions of the variances are symmetric. Finally, simulations for epidemics spreading on networks are performed to confirm our analytical results. We find a close agreement between the simulations and theoretical predictions.<\/jats:p>","DOI":"10.3390\/sym15101813","type":"journal-article","created":{"date-parts":[[2023,9,24]],"date-time":"2023-09-24T10:40:22Z","timestamp":1695552022000},"page":"1813","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of Competitive Two-Strain Stochastic SIR Epidemics on Heterogeneous Networks"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiaojie","family":"Jing","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China"},{"name":"Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9362-5859","authenticated-orcid":false,"given":"Guirong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China"},{"name":"Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1098\/rspa.1927.0118","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","author":"Kermack","year":"1927","journal-title":"Proc. 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