A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach

De Pillis, L. G.; Radunskaya, A.

doi:10.1080/10273660108833067

Title: A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach

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Abstract

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.

Authors:

De Pillis, L. G. ^[1]; Radunskaya, A. ^[2]

Harvey Mudd College, Claremont, CA 91711, USA, Argonne National Laboratory, Argonne, IL 60439, USA
Pomona College, Claremont, CA 91711, USA

Publication Date:: Mon Jan 01 00:00:00 EST 2001

Sponsoring Org.:: USDOE

OSTI Identifier:: 1198190

Grant/Contract Number:: W-3 1-109-ENG-38

Resource Type:: Published Article

Journal Name:: Journal of Theoretical Medicine

Additional Journal Information:: Journal Name: Journal of Theoretical Medicine Journal Volume: 3 Journal Issue: 2; Journal ID: ISSN 1027-3662

Publisher:: Hindawi Publishing Corporation

Country of Publication:: Country unknown/Code not available

Language:: English

Citation Formats


                    De Pillis, L. G., and Radunskaya, A. A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach.  Country unknown/Code not available: N. p., 2001. 
Web.  doi:10.1080/10273660108833067.

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                    De Pillis, L. G., & Radunskaya, A. A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach.  Country unknown/Code not available.  https://doi.org/10.1080/10273660108833067

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                    De Pillis, L. G., and Radunskaya, A. Mon .  
"A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach".  Country unknown/Code not available.  https://doi.org/10.1080/10273660108833067.

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@article{osti_1198190,

  title        = {A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach},

  author       = {De Pillis, L. G. and Radunskaya, A.},

  abstractNote = {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.},

  doi          = {10.1080/10273660108833067},

  journal      = {Journal of Theoretical Medicine},

  number       = 2,

  volume       = 3,

  place        = {Country unknown/Code not available},

  year         = {Mon Jan 01 00:00:00 EST 2001},

  month        = {Mon Jan 01 00:00:00 EST 2001}

}

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