{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:06:27Z","timestamp":1753880787539,"version":"3.41.2"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12471160"],"award-info":[{"award-number":["12471160"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"crossref","award":["2024A1515011425"],"award-info":[{"award-number":["2024A1515011425"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:p> This paper establishes a 16-dimensional multiscale COVID-19 model with three geographical regions and interval parameters, and the model can be investigated by a slow\u2013fast system. In the fast subsystem, there is a globally asymptotically stable equilibrium. The fast\u2013slow theory is applied to investigate the stability and bifurcations of Disease-Free Equilibrium (DFE) and Endemic Equilibrium (EE) of the slow subsystem. It is found that transmission rates in three geographical regions, proportion and average time of individuals spend in public places can result in forward and backward bifurcations. Some criteria for verifying whether the system has forward and backward bifurcations are presented. When there is backward bifurcation, stable DFE coexists with stable EE for [Formula: see text]; slow subsystem has saddle-node bifurcation when [Formula: see text]; with respect to EE, the subsystem has pitchfork bifurcation when [Formula: see text]. Interestingly, a critical value [Formula: see text] of the average time [Formula: see text] is obtained from individuals in public places. The dynamics of slow subsystem are appropriate to that of the multiscale system. Chaotic dynamics are found in the multiscale system due to seasonal and stochastic infection. Moreover, several numerical analyses of COVID-19 for Hong Kong and South Africa agree with the theoretical results. <\/jats:p>","DOI":"10.1142\/s0218127425501056","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T13:59:08Z","timestamp":1749045548000},"source":"Crossref","is-referenced-by-count":0,"title":["Dynamics in a Multiscale COVID-19 Model with Three Geographical Regions"],"prefix":"10.1142","volume":"35","author":[{"given":"Jiabing","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China"}]},{"given":"Qigui","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. 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