{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T17:56:06Z","timestamp":1774288566437,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T00:00:00Z","timestamp":1751500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo (ANID) of Chile","award":["1231256"],"award-info":[{"award-number":["1231256"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness of solutions with the defined conditions using integral equations. On top of that, an auxiliary result is established, outlining the relationship between the unknown function values in the deviation argument and the time parameter. The stability analysis is conducted using the Lyapunov\u2013Razumikhin method, adapted for differential equations with a piecewise constant argument of the generalized type. The trivial equilibrium\u2019s stability is examined, and the stability of the positive equilibrium is assessed by transforming it into a trivial form. Finally, sufficient conditions for the uniform asymptotic stability of both the trivial and positive equilibria are established.<\/jats:p>","DOI":"10.3390\/axioms14070514","type":"journal-article","created":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T06:54:16Z","timestamp":1751525656000},"page":"514","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Existence and Global Exponential Stability of Equilibrium for an Epidemic Model with Piecewise Constant Argument of Generalized Type"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3823-5898","authenticated-orcid":false,"given":"Kuo-Shou","family":"Chiu","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad Metropolitana de Ciencias de la Educaci\u00f3n, Jos\u00e9 Pedro Alessandri 774, Santiago 7760197, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6515-6880","authenticated-orcid":false,"given":"Fernando","family":"C\u00f3rdova-Lepe","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, F\u00edsica y Estad\u00edstica, Universidad Cat\u00f3lica del Maule, Talca 3480112, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,3]]},"reference":[{"key":"ref_1","first-page":"253","article-title":"Stability analysis for a vector disease model","volume":"7","author":"Cooke","year":"1979","journal-title":"Rocky Mt. 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