{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:52:49Z","timestamp":1773795169375,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tecnologico Nacional de Mexico\/IT Tijuana","award":["13886.22-P"],"award-info":[{"award-number":["13886.22-P"]}]},{"name":"Tecnologico Nacional de Mexico\/IT Tijuana","award":["13747.22-P"],"award-info":[{"award-number":["13747.22-P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper deals with a recently reported mathematical model formulated by five first-order ordinary differential equations that describe glucoregulatory dynamics. As main contributions, we found a localization domain with all compact invariant sets; we settled on sufficient conditions for the existence of a bounded positively-invariant domain. We applied the localization of compact invariant sets and Lyapunov\u2019s direct methods to obtain these results. The localization results establish the maximum cell concentration for each variable. On the other hand, Lyapunov\u2019s direct method provides sufficient conditions for the bounded positively-invariant domain to attract all trajectories with non-negative initial conditions. Further, we illustrate our analytical results with numerical simulations. Overall, our results are valuable information for a better understanding of this disease. Bounds and attractive domains are crucial tools to design practical applications such as insulin controllers or in silico experiments. In addition, the model can be used to understand the long-term dynamics of the system.<\/jats:p>","DOI":"10.3390\/axioms11070320","type":"journal-article","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T20:53:02Z","timestamp":1656622382000},"page":"320","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9839-4711","authenticated-orcid":false,"given":"Diana","family":"Gamboa","sequence":"first","affiliation":[{"name":"Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Tijuana, Blvd. Alberto Lim\u00f3n Padilla s\/n, Tijuana 22454, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1219-0433","authenticated-orcid":false,"given":"Luis N.","family":"Coria","sequence":"additional","affiliation":[{"name":"Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Tijuana, Blvd. Alberto Lim\u00f3n Padilla s\/n, Tijuana 22454, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6567-1065","authenticated-orcid":false,"given":"Paul A.","family":"Valle","sequence":"additional","affiliation":[{"name":"Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Tijuana, Blvd. Alberto Lim\u00f3n Padilla s\/n, Tijuana 22454, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108086","DOI":"10.1016\/j.diabres.2020.108086","article-title":"Mortality Attributable to Diabetes in 20\u201379 Years Old Adults, 2019 Estimates: Results from the International Diabetes Federation Diabetes Atlas","volume":"162","author":"Saeedi","year":"2020","journal-title":"Diabetes Res. 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