Abstract
A pulsed chemotherapeutic treatment model is investigated in this work. We prove the existence of nontrivial periodic solutions by the mean of Lyapunov-Schmidt bifurcation method of a cancer model. In this model we consider the case of application of two drugs, the first one P with continuous effect, it appears in the differential equations, and the second one T with instantaneous effects expressed by impulse equations. The existence of bifurcated nontrivial periodic solutions are discussed with respect to the competition parameter values.
Highlights
In this work a mathematical model for cancer chemotherapy is studied by considering interactions between tumor and normal cells
We prove the existence of nontrivial periodic solutions by the mean of Lyapunov-Schmidt bifurcation method of a cancer model
In this model we consider the case of application of two drugs, the first one P with continuous effect, it appears in the differential equations, and the second one T with instantaneous effects expressed by impulse equations
Summary
In this work a mathematical model for cancer chemotherapy is studied by considering interactions between tumor and normal cells. This model consists of three nonlinear ordinary differential equations describing the dynamic of the cancer under the continuous effect of a drug P, and three discrete equations describing the instantaneous effects of a drug T on the different types of cancerous cells, it is called pulsed-therapy. We use similar approach to that used in [7] to find conditions of stability of trivial solution and bifurcation of nontrivial periodic solutions corresponding to eradication of the tumor and its persistence, respectively. In section four we study the stability of trivial solution and the bifurcation of periodic nontrivial solutions.
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