{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:09:12Z","timestamp":1770833352171,"version":"3.50.1"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,9,15]]},"abstract":"<jats:p> In this paper, we propose a delayed mathematical model describing oncolytic virotherapy treatment of a tumour that proliferates according to the logistic growth function, incorporating viral lytic cycle. The tumour population cells are divided into uninfected and infected cell sub-populations and the virus spreading is supposed to be in a direct mode (i.e. from cell to cell). Depending on the time delay, we analyze the positivity and boundedness of solutions and the stability of tumour, infected and uninfected free equilibria (TFE, IFE, UFE) and uninfected\u2013infected equilibrium (UIE) is established. We prove that, delay can lead to \u201cJeff\u2019s phenomenon\u201d observed in a laboratory which causes oscillations in tumour size whose phase and period change over time. With nonlinear dependence of UIE equilibrium on time delay, we develop a more general algorithm determining the stability\/instability of the oscillating periodic solutions bifurcating from the UIE equilibrium. Finally, we present numerical simulations illustrating our theoretical results. <\/jats:p>","DOI":"10.1142\/s0218127422501711","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T08:12:40Z","timestamp":1664439160000},"source":"Crossref","is-referenced-by-count":7,"title":["Hopf Bifurcation in Oncolytic Therapeutic Modeling: Viruses as Anti-Tumor Means with Viral Lytic Cycle"],"prefix":"10.1142","volume":"32","author":[{"given":"Fatiha","family":"Najm","sequence":"first","affiliation":[{"name":"Department of Mathematics Faculty of Sciences, Ibn Tofail University Campus Universitaire, BP 133, K\u00e9nitra, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9824-9036","authenticated-orcid":false,"given":"Radouane","family":"Yafia","sequence":"additional","affiliation":[{"name":"Department of Mathematics Faculty of Sciences, Ibn Tofail University Campus Universitaire, BP 133, K\u00e9nitra, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. 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