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- W2463653554 abstract "This paper combines an idea of d’Onofrio [2], [3] for modeling tumor-immune system competition and immunotherapy with Udriste theory [6]-[8] of the geometric dynamics. Section 1 refines the tumor-immune flow. Section 2 describes the critical points of energy and formulates two criteria for nonexistence of periodic orbits. Section 3 analyzes the least squares technique for a flow and a geometric structure. Section 4 studies the linearization of tumor-immune geometric dynamics. Section 5 underlines the novelty of our results. Key–Words: Tumor-immune ODEs, competition of cells, equilibrium points, geometric dynamics. 1 The d’Onofrio flow The nonlinear dynamical system used by d’Onofrio [2], [3] to model the competition between tumor and immune cells has the form dx dt (t) = ax(t)F (x(t))− μφ(x(t))x(t)y(t) dy dt (t) = −y(t)ψ(x(t)) + bq(x(t)) , (1) where x(t) ≥ 0 is the density of tumor cells, y(t) ≥ 0 is the density of lymphocyte population, the functions F, φ, ψ, q are of class C1 and ψ(0) > 0, |ψ′(x)| ≤ 1 F (0) > 0, F ′(x) ≤ 0, F ′(0) = 0, lim x→0 xF (x) = 0 φ(x) > 0, φ′(x) ≤ 0, φ′(0) = 0, lim x→0 xF (x) = ` q(0) = 1, |q′(x)| ≤ 1. The parameter μ plays an important role for modeling the cells competition. When μ = 0, tumor cells grows according to the law ∫ x(t)" @default.
- W2463653554 created "2016-07-22" @default.
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- W2463653554 date "2009-05-30" @default.
- W2463653554 modified "2023-09-27" @default.
- W2463653554 title "Geometric dynamics of d'Onofrio model of tumor-immune system competition" @default.
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