Schattler2016 - Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy

A minimally parameterized mathematical model for low-dose metronomic
chemotherapy is formulated that takes into account angiogenic signaling between
the tumor and its vasculature and tumor inhibiting effects of tumor-immune system
interactions. The dynamical equations combine a model for tumor development under
angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune
system interactions by Stepanova. The dynamical properties of the model are analyzed.
Depending on the parameter values, the system encompasses a variety of medically
realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy
is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium
point) to situations when (ii) tumor dormancy is induced (a unique, globally asymp-
totically stable benign equilibrium point exists) to (iii) multi-stable situations that have
both persistent benign and malignant behaviors separated by the stable manifold of
an unstable equilibrium point and finally to (iv) situations when tumor growth can-
not be overcome by low-dose metronomic chemotherapy. The model forms a basis
for a more general study of chemotherapy when the main components of a tumor’s
microenvironment are taken into account