ArticleJournal of mathematical biology2003
A delay differential equation model for tumor growth.
Article in Journal of mathematical biology, 2003. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 22 papers.
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Who cites it
22 citing papers in PubMed, 284 citations in OpenAlex.
- The impact of tumor microenvironment and treatment schedule on the effectiveness of radiation therapy.PloS one · 2025Article
- Disquisition on convergence, stability, and data dependence for a new fast iterative process.Scientific reports · 2024Article
- Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation.Journal of mathematical biology · 2024Article
- Radiation necrosis after radiation therapy treatment of brain metastases: A computational approach.PLoS computational biology · 2024Article
- The Existence of Periodic Solutions for Second-Order Delay Differential Systems.Journal of dynamics and differential equations · 2022Article
- Optimal regulation of tumour-associated neutrophils in cancer progression.Royal Society open science · 2022Article
- A novel mathematical model of heterogeneous cell proliferation.Journal of mathematical biology · 2021Article
- In silico trials predict that combination strategies for enhancing vesicular stomatitis oncolytic virus are determined by tumor aggressivity.Journal for immunotherapy of cancer · 2021Article
- Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system.Nonlinear dynamics · 2021Article
- Global Dynamics of a Breast Cancer Competition Model.Differential equations and dynamical systems · 2020Article
- Different ODE models of tumor growth can deliver similar results.BMC cancer · 2020Article
- Mathematical Modelling for the Role of CD4Computational and mathematical methods in medicine · 2020Article
- Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer.Mathematical medicine and biology : a journal of the IMA · 2019Article
- Dynamics of Breast Cancer under Different Rates of Chemoradiotherapy.Computational and mathematical methods in medicine · 2019Article
- Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology.Frontiers in immunology · 2019Review
- The finite state projection approach to analyze dynamics of heterogeneous populations.Physical biology · 2017Article
- Tumour chemotherapy strategy based on impulse control theory.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2017Article
- Article
- Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.Journal of pharmacokinetics and pharmacodynamics · 2014Article
- Delay differential model for tumour-immune response with chemoimmunotherapy and optimal control.Computational and mathematical methods in medicine · 2014Article
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Authors and funding
2 authors at 2 institutions in 2 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We analyze the stability of the system and prove a theorem based on the argument principle to determine the stability of a fixed point and show that the stability may depend on the delay. We show theoretically and through numerical simulations that periodic solutions may arise through Hopf Bifurcations.
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