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Set-Valued Control of Cancer by Combination Chemotherapy

Year 2023, , 7 - 16, 30.04.2023
https://doi.org/10.33187/jmsm.1069549

Abstract

A mathematical model of ordinary differential equations is considered to analyze the pharmacokinetics of multi-chemotherapeutic drugs and their pharmacodynamic effects on homogeneous tumors. Set-valued analysis is used to design protocols of drug administration and applied to decrease tumor density under their carrying capacity of Gompertz growth and converge to zero.




References

  • [1] Y. Batmani, H. Khaloozadeh, Multi objective optimization of drug regimens in cancer chemotherapy using a PK-PD model, 19th Iranian Conference on Electrical Engineering, (2011), 1-1.
  • [2] A. Floares, C. Floares, M. Cucu, L. Lazar, Adaptive neural networks control of drug dosage regimens in cancer chemotherapy, Proceedings of the International Joint Conference on Neural Networks, 1 (2003), 154-159.
  • [3] M. M. Hadjiandreou, G. D. Mitsis, Mathematical modeling of tumor growth, drug-resistance, toxicity, and optimal therapy design, IEEE Trans. Biomed. Eng., 61(2) (2014), 415-425.
  • [4] A. Petrovski, J. McCall, B. Sudha, Multi-objective optimization of cancer chemotherapy using swarm intelligence, AISB Symposium on Adaptive and Emergent Behaviour and Complex Systems, UK Society for AI, (2009).
  • [5] A. Petrovski, J. McCall, Multi-objective optimisation of cancer chemotherapy using evolutionary algorithms, International Conference on Evolutionary Multi-Criterion Optimization, Springer, Berlin, Heidelberg, (2001).
  • [6] J. McCall, Genetic algorithms for modelling and optimisation, J. Comput. Appl., 184(1) (2005), 205-222.
  • [7] H. Khaloozadeh, Y. Pedram, H. S. Fatemeh, The optimal dose of CAF regimen in adjuvant chemotherapy for breast cancer patients at stage IIB, Math. Biosci., 213(2) (2008), 151-158.
  • [8] T. Ajayi, S. Hosseinian, A. J. Schaefer, C. D. Fuller, Combination Chemotherapy Optimization with Discrete Dosing, arXiv preprint, (2021).
  • [9] A. Petrovski, An application of genetic algorithms to chemotherapy treatment, Ph.D. Thesis, Robert Gordon University, 1998.
  • [10] S. L. Thomson, G. Ochoa, The Local Optima Level in Chemotherapy Schedule Optimisation, European Conference on Evolutionary Computation in Combinatorial Optimization (Part of EvoStar), Springer, Cham, (2020).
  • [11] K. Kassara, A unified set-valued approach to control immunotherapy, SIAM J. Control Optim., 48 (2009), 909-924.
  • [12] M. Serhani, H. Essaadi, K. Kassara, A. Boutoulout, Control by viability in a chemotherapy cancer model, Acta Biotheor., 67 (2019), 177-200.
  • [13] K. Kassara, A. Moustafid, Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method, Math. Biosci., 231 (2011), 135-143.
  • [14] A. Moustafid, General Anti-Angiogenic Therapy Protocols with Chemotherapy, Int. J. Math. Model. Computations, 11(3) (2021).
  • [15] A. Moustafid, General chemotherapy protocols, J. Appl. Dynamic Syst. Control, 4 (2021), 18-25.
  • [16] L. Boujallal, O. Balatif, M. Elhia, A set-valued approach applied to a control problem of tuberculosis with treatment, IMA J. Math. Control Inf., 38 (2021), 1010-1027.
  • [17] M. Elhia, L. Boujallal, M. Alkama, O. Balatif, M. Rachik, Set-valued control approach applied to a COVID-19 model with screening and saturated treatment function, Complexity, (2020).
  • [18] L. Boujallal, M. Elhia, O. Balatif, A novel control set-valued approach with application to epidemic models, J. Appl. Math. Comput., 65 (2021), 295-319.
  • [19] J. P. Aubin, Dynamic Economic Theory: A Viability Approach, Springer, Berlin, 1997.
  • [20] A. Iliadis, Optimizing drug regimens in cancer chemotherapy, Basic Clin. Pharmacol. Toxicol., 96(3) (2005), 269-270.
Year 2023, , 7 - 16, 30.04.2023
https://doi.org/10.33187/jmsm.1069549

Abstract

References

  • [1] Y. Batmani, H. Khaloozadeh, Multi objective optimization of drug regimens in cancer chemotherapy using a PK-PD model, 19th Iranian Conference on Electrical Engineering, (2011), 1-1.
  • [2] A. Floares, C. Floares, M. Cucu, L. Lazar, Adaptive neural networks control of drug dosage regimens in cancer chemotherapy, Proceedings of the International Joint Conference on Neural Networks, 1 (2003), 154-159.
  • [3] M. M. Hadjiandreou, G. D. Mitsis, Mathematical modeling of tumor growth, drug-resistance, toxicity, and optimal therapy design, IEEE Trans. Biomed. Eng., 61(2) (2014), 415-425.
  • [4] A. Petrovski, J. McCall, B. Sudha, Multi-objective optimization of cancer chemotherapy using swarm intelligence, AISB Symposium on Adaptive and Emergent Behaviour and Complex Systems, UK Society for AI, (2009).
  • [5] A. Petrovski, J. McCall, Multi-objective optimisation of cancer chemotherapy using evolutionary algorithms, International Conference on Evolutionary Multi-Criterion Optimization, Springer, Berlin, Heidelberg, (2001).
  • [6] J. McCall, Genetic algorithms for modelling and optimisation, J. Comput. Appl., 184(1) (2005), 205-222.
  • [7] H. Khaloozadeh, Y. Pedram, H. S. Fatemeh, The optimal dose of CAF regimen in adjuvant chemotherapy for breast cancer patients at stage IIB, Math. Biosci., 213(2) (2008), 151-158.
  • [8] T. Ajayi, S. Hosseinian, A. J. Schaefer, C. D. Fuller, Combination Chemotherapy Optimization with Discrete Dosing, arXiv preprint, (2021).
  • [9] A. Petrovski, An application of genetic algorithms to chemotherapy treatment, Ph.D. Thesis, Robert Gordon University, 1998.
  • [10] S. L. Thomson, G. Ochoa, The Local Optima Level in Chemotherapy Schedule Optimisation, European Conference on Evolutionary Computation in Combinatorial Optimization (Part of EvoStar), Springer, Cham, (2020).
  • [11] K. Kassara, A unified set-valued approach to control immunotherapy, SIAM J. Control Optim., 48 (2009), 909-924.
  • [12] M. Serhani, H. Essaadi, K. Kassara, A. Boutoulout, Control by viability in a chemotherapy cancer model, Acta Biotheor., 67 (2019), 177-200.
  • [13] K. Kassara, A. Moustafid, Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method, Math. Biosci., 231 (2011), 135-143.
  • [14] A. Moustafid, General Anti-Angiogenic Therapy Protocols with Chemotherapy, Int. J. Math. Model. Computations, 11(3) (2021).
  • [15] A. Moustafid, General chemotherapy protocols, J. Appl. Dynamic Syst. Control, 4 (2021), 18-25.
  • [16] L. Boujallal, O. Balatif, M. Elhia, A set-valued approach applied to a control problem of tuberculosis with treatment, IMA J. Math. Control Inf., 38 (2021), 1010-1027.
  • [17] M. Elhia, L. Boujallal, M. Alkama, O. Balatif, M. Rachik, Set-valued control approach applied to a COVID-19 model with screening and saturated treatment function, Complexity, (2020).
  • [18] L. Boujallal, M. Elhia, O. Balatif, A novel control set-valued approach with application to epidemic models, J. Appl. Math. Comput., 65 (2021), 295-319.
  • [19] J. P. Aubin, Dynamic Economic Theory: A Viability Approach, Springer, Berlin, 1997.
  • [20] A. Iliadis, Optimizing drug regimens in cancer chemotherapy, Basic Clin. Pharmacol. Toxicol., 96(3) (2005), 269-270.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Amine Moustafid 0000-0002-9121-0745

Publication Date April 30, 2023
Submission Date February 7, 2022
Acceptance Date October 27, 2022
Published in Issue Year 2023

Cite

APA Moustafid, A. (2023). Set-Valued Control of Cancer by Combination Chemotherapy. Journal of Mathematical Sciences and Modelling, 6(1), 7-16. https://doi.org/10.33187/jmsm.1069549
AMA Moustafid A. Set-Valued Control of Cancer by Combination Chemotherapy. Journal of Mathematical Sciences and Modelling. April 2023;6(1):7-16. doi:10.33187/jmsm.1069549
Chicago Moustafid, Amine. “Set-Valued Control of Cancer by Combination Chemotherapy”. Journal of Mathematical Sciences and Modelling 6, no. 1 (April 2023): 7-16. https://doi.org/10.33187/jmsm.1069549.
EndNote Moustafid A (April 1, 2023) Set-Valued Control of Cancer by Combination Chemotherapy. Journal of Mathematical Sciences and Modelling 6 1 7–16.
IEEE A. Moustafid, “Set-Valued Control of Cancer by Combination Chemotherapy”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 1, pp. 7–16, 2023, doi: 10.33187/jmsm.1069549.
ISNAD Moustafid, Amine. “Set-Valued Control of Cancer by Combination Chemotherapy”. Journal of Mathematical Sciences and Modelling 6/1 (April 2023), 7-16. https://doi.org/10.33187/jmsm.1069549.
JAMA Moustafid A. Set-Valued Control of Cancer by Combination Chemotherapy. Journal of Mathematical Sciences and Modelling. 2023;6:7–16.
MLA Moustafid, Amine. “Set-Valued Control of Cancer by Combination Chemotherapy”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 1, 2023, pp. 7-16, doi:10.33187/jmsm.1069549.
Vancouver Moustafid A. Set-Valued Control of Cancer by Combination Chemotherapy. Journal of Mathematical Sciences and Modelling. 2023;6(1):7-16.

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