The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach
Open accessAbstract
We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four‐population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug‐free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor‐drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy regimens. Using optimal control theory with constraints and numerical simulations, we obtain new therapy protocols that we then compare with traditional pulsed periodic treatment. The optimal control generated therapies produce larger oscillations in the tumor population over time. However, by the end of the treatment period, total tumor size is smaller than that achieved through traditional pulsed therapy, and the normal cell population suffers nearly no oscillations.
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Cites
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A stochastic model for the origin and treatment of tumors containing drug-resistant cells
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Cited by
The mathematics of cancer: integrating quantitative models
Altrock, P. M., Liu, L. L., & Michor, F. (2015) · Nature Reviews Cancer · doi:10.1038/nrc4029 · Cited by 685
A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth
de Pillis, L. G., Radunskaya, A. E., & Wiseman, C. L. (2005) · Cancer Research · doi:10.1158/0008-5472.can-05-0564 · Cited by 649
Self-citationA cellular automata model of tumor–immune system interactions
Mallet, D. G., & De Pillis, L. G. (2006) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2005.08.002 · Cited by 255
Self-citationBarish, S., Ochs, M. F., Sontag, E. D., & Gevertz, J. L. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1703355114 · Cited by 48
Data-Driven Mathematical Model of Osteosarcoma
Le, T., Su, S., Kirshtein, A., & Shahriyari, L. (2021) · Cancers · doi:10.3390/cancers13102367 · Cited by 39
Metadata
- Authors
- De Pillis, L. G., & Radunskaya, A.
- Venue
- Computational and Mathematical Methods in Medicine
- Publisher
- Wiley
- Published
- 2000-04-18
- Volume
- 3
- Issue
- 2
- Pages
- 79-100
- ISSN
- 1748-670X (ISSN-L)
- 1748-6718
- OpenAlex
- W2013304036
- Cited by
- 425
- References
- 14
- FWCI
- 2.96
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- De Pillis, L. G., & Radunskaya, A. (2001). A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach. Computational and Mathematical Methods in Medicine. https://doi.org/10.1080/10273660108833067
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
