{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T10:08:43Z","timestamp":1779098923885,"version":"3.51.4"},"posted":{"date-parts":[[2025,11,4]]},"reference-count":0,"publisher":"Wiley","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A new system of delayed differential equations for tumor-immune system\ninteractions is proposed and studied. The system describes the\ninteractions between tumor cells and the immune system, at the most\naggressive phase of cancer, where tumor cells have developed mechanisms\nfrom earlier stages to evade immune responses. The model incorporates\nadoptive cellular immunotherapy as the only effective treatment, and\naccounts for the complex influence of interleukins. To render the model\nmore biologically realistic, it also includes a time delay representing\nthe lag between the interaction of tumor cells and activated immune\ncells and the subsequent effectiveness of the immune response. These\naspects, captured together, reflect the biological novelty of our\napproach. We first establish the well-posedness of the system, proving\nthe global existence of the solution and its positivity. Then, we focus\non the equilibrium states of the system, their asymptotic stability, and\nhow the delay affects the stability of the equilibrium states and the\nbehaviour of the solution. We investigate the global stability of a\ntumor equilibrium state with biological relevance, and estimate the\nlength of the delay that preserves the stability of a tumor-free\nequilibrium. These results ensure the mathematical consistency of the\nmodel and provide a solid theoretical basis for analysing how delayed\nimmune responses can influence the long-term behaviour of the tumor\nprogression. Finally, we conduct some numerical simulations of the\ndelayed system in order to illustrate the theoretical analysis and\ninvestigate the impact of the delay. We interpret the results and\nexplore their biological implications in the context of cancer\nprogression.<\/jats:p>","DOI":"10.22541\/au.176228650.02560091\/v1","type":"posted-content","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T20:01:49Z","timestamp":1762286509000},"source":"Crossref","is-referenced-by-count":0,"title":["Mathematical analysis and simulations of a cancer model with interleukins and delayed immunotherapy"],"prefix":"10.22541","author":[{"given":"Laid","family":"Boudjellal","sequence":"first","affiliation":[{"name":"Universidade do Minho"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4771-9859","authenticated-orcid":false,"given":"Ana","family":"Soares","sequence":"additional","affiliation":[{"name":"Universidade do Minho"}]},{"given":"Maria Joana","family":"Torres","sequence":"additional","affiliation":[{"name":"Universidade do Minho"}]}],"member":"311","container-title":[],"original-title":[],"link":[{"URL":"https:\/\/www.authorea.com\/doi\/pdf\/10.22541\/au.176228650.02560091\/v1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T09:17:31Z","timestamp":1779095851000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.authorea.com\/doi\/full\/10.22541\/au.176228650.02560091\/v1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.22541\/au.176228650.02560091\/v1","relation":{"is-preprint-of":[{"id-type":"doi","id":"10.1002\/mma.70757","asserted-by":"subject"}]},"subject":[],"published":{"date-parts":[[2025,11,4]]},"subtype":"preprint"}}