{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T18:11:25Z","timestamp":1784052685682,"version":"3.55.0"},"reference-count":42,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T00:00:00Z","timestamp":1783987200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>\n                    We rigorously analyze the dynamic properties of Kermack-McKendrick-like compartmental models for infectious diseases, extending the classical SIR framework to include exposed individuals, mild and severe infections, hospitalization, and intensive care unit (ICU) compartments. Using a 13-compartment model, we establish mathematical results on well-posedness, the basic reproduction number\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    , a first integral leading to a unique final epidemic size, and the global stability of the disease-free equilibrium under permanent immunity. When temporary immunity is included, we prove the existence of an endemic equilibrium for\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    \u2009&gt;\u20091. An age-stratified multi-group version of the model is also studied, demonstrating similar convergence properties and highlighting the impact of age structure on epidemic dynamics. Our results provide a rigorous mathematical framework for understanding how immunity duration, clinical progression, and age structure shape epidemic outcomes.\n                  <\/jats:p>","DOI":"10.1371\/journal.pone.0352960","type":"journal-article","created":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T17:45:37Z","timestamp":1784051137000},"page":"e0352960","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic properties of Kermack-McKendrick-like models"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-3797-579X","authenticated-orcid":true,"given":"Hamidou 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