Cell kinetic modelling and the chemotherapy of cancer
Cell kinetic modelling and the chemotherapy of cancer
Differential equations and dynamical systems
Differential equations and dynamical systems
Optimal control drug scheduling of cancer chemotherapy
Automatica (Journal of IFAC)
Three-dimensional competitive Lotka-Volterra systems with no periodic orbits
SIAM Journal on Applied Mathematics
Optimal control applied to cell-cycle-specific cancer chemotherapy
SIAM Journal on Applied Mathematics
Optimizing drug regimens in cancer chemotherapy by an efficacy—toxicity mathematical model
Computers and Biomedical Research
Modeling tumor regrowth and immunotherapy
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
The influence of fixed and free final time of treatment on optimal chemotherapeutic protocols
Mathematical and Computer Modelling: An International Journal
The dynamics of growth-factor-modified immune response to cancer growth: One dimensional models
Mathematical and Computer Modelling: An International Journal
Singularity of optimal control in some problems related to optimal chemotherapy
Mathematical and Computer Modelling: An International Journal
A simple mathematical model and alternative paradigm for certain chemotherapeutic regimens
Mathematical and Computer Modelling: An International Journal
BIOCOMPUCHEM'09 Proceedings of the 3rd WSEAS International Conference on Computational Chemistry
Modeling and optimization of combined cytostatic and cytotoxic cancer chemotherapy
Artificial Intelligence in Medicine
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We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. We show that the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once traatment has stopped. We present numerical experiments in which optimal control therapy is able to drive the system into a desirable basin of attraction, whereas traditional pulsed chemotherapy is not.