Modelling Heterogeneous Tumor Elimination or its Recurrence with ODE

Khadija El-Matteli (1) , Ines Abdeljaoued-Tej (1, 2)

1 BIMS Laboratory - LR16IPT09, Institut Pasteur de Tunis, University Tunis-El-Mana, Tunisia
2 University of Carthage, ESSAI, Ariana, Tunisia

We present a new mathematical model, in the form of a system of ordinary differential equations (ODEs), governing the growth of cancer at the level of the cell population combined with treatment by the immune system or chemotherapy. This model describes the kinetic relationships between different states and cell types. Besides, it will be about presenting a mathematical analyse. The principal objective of this work is to study the recurrence, coexistence, and elimination of cells cancerous, under the assumption of a heterogeneous tumor. Also, we aim to study the influence of cancer stem cells on its dynamics and characterize the subsequent impact on the availability of factors that help tumor growth and resistance to treatment.

Mots clés: Global dynamic of the full system Competition model Tumor-Immune dynamic Stability analysis Differentiation Immune system Chemotherapy; Global dynamic of the full system; Competition model; Tumor-Immune dynamic; Stability analysis; Differentiation; Immune system; Chemotherapy

Domaines: Intelligence artificielle [cs.AI]; Bio-informatique [q-bio.QM]; Théorie des groupes [math.GR]; Anneaux et algèbres [math.RA]; Statistiques [math.ST]; Ingénierie, finance et science [cs.CE]; Informatique et langage [cs.CL]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Synthèse d'image et réalité virtuelle [cs.GR]; Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]; Analyse classique [math.CA]; Systèmes dynamiques [math.DS]

Khadija El-Matteli, Ines Abdeljaoued-Tej. Modelling Heterogeneous Tumor Elimination or its Recurrence with ODE. LR16IPT09, Institut Pasteur de Tunis, University Tunis-El-Manar, Tunisia. 2019. ⟨hal-04895388⟩