Abstract
In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give sufficient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.
Highlights
Once tumor spheroids reach the blood stream, the process of vascularization called angiogenesis begins, see [3]
We extend results presented in [4], proving the existence of periodic dynamics for periodical continuous drug dose under certain conditions on the parameters
For the reader’s convenience we first recall some basic facts about cooperative systems that will be used for proving our results
Summary
Once tumor spheroids reach the blood stream, the process of vascularization called angiogenesis begins, see [3]. [2] considers periodic treatment, it does not provide general results of existence of periodic solutions. We say that a pair of T -periodic differentiable functions (a(t), b(t)) is a sub-solution pair of (2) if a ≤ f(t, a(t), b(t)), b ≤ g(t, a(t), b(t)), for all t. An important feature for cooperative system (2) related to periodic orbits was established in [6], Theorem 2.1.
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