A mathematical approach with delay kernel for the role of the immune response time delay in periodic therapy of the tumors

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dc.creatorMircea, G.
dc.creatorNeamtu, M.
dc.creatorHorhat, R. F.
dc.creatorOpris, D.
dc.date2006-10-23
dc.date.accessioned2026-07-07T07:29:18Z
dc.date.available2026-07-07T07:29:18Z
dc.descriptionWe consider the model of interaction between the immune system and tumor cells including a memory function that reflect the influence of the past states, to simulate the time needed by the latter to develop a chemical and cell mediated response to the presence of the tumor. The memory function is called delay kernel. The results are compared with those from other papers, concluding that the memory function introduces new instabilities in the system leading to an uncontrolable growth of the tumor. If the coefficient of the memory function is used as a bifurcation parameter, it is found that Hopf bifurcation occurs for kernel. The direction and stability of the bifurcating periodic solutions are determined. Some numerical simulations for justifying the theoretical analysis are also given.
dc.description22 pages, 9 figures, the paper was presented at "Conference Francophone sur la Modelisation Mathematique en Biologie et en Medecine", Craiova, Romania,12-14 July, 2006
dc.identifierhttps://arxiv.org/abs/math/0610656
dc.identifierhttp://arxiv.org/abs/math/0610656
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118053
dc.subjectDynamical Systems
dc.titleA mathematical approach with delay kernel for the role of the immune response time delay in periodic therapy of the tumors
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