ArticleJournal of mathematical biology2016
Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.
Article in Journal of mathematical biology, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Mathematical analysis of metronomic chemotherapy response in metastatic gastrointestinal cancer: identifying critical parameters from clinical data.Scientific reports · 2026Article
- A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation.eLife · 2023Article
- Normalizing tumor microenvironment with nanomedicine and metronomic therapy to improve immunotherapy.Journal of controlled release : official journal of the Controlled Release Society · 2022Article
- Modeling and Analysis of Breast Cancer with Adverse Reactions of Chemotherapy Treatment through Fractional Derivative.Computational and mathematical methods in medicine · 2022Article
- Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives.Mathematical biosciences and engineering : MBE · 2021Article
- Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance.Frontiers in immunology · 2020Article
- Modeling treatment-dependent glioma growth including a dormant tumor cell subpopulation.BMC cancer · 2018Article
- Role of vascular normalization in benefit from metronomic chemotherapy.Proceedings of the National Academy of Sciences of the United States of America · 2017Article
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Authors and funding
3 authors.
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Abstract
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 asymptotically 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 cannot 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.
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