Research Article
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Year 2023, Volume: 6 Issue: 1, 40 - 56, 16.06.2023
https://doi.org/10.53508/ijiam.1211906

Abstract

References

  • El Haout, S., Fatani, M., Farha, N., AlSawaftah, N., Mortula, M., Husseini, G.: Modeling the Effects of Chemotherapy and Immunotherapy on Tumor Growth. Journal Of Biomedical Nanotechnology. 17, 2505-2518, 2021
  • Pratap, J.: An optimal control strategy for mathematically modeling cancer combination therapy. ArXiv Preprint ArXiv:2101.12120, 2021
  • Nave, O.: A mathematical model for treatment using chemo-immunotherapy. Heliyon. 8, e09288, 2022
  • Unni, P., Seshaiyer, P.: Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions. Computational And Mathematical Methods In Medicine, 2019
  • Sharma, S., Samanta, G.: Analysis of the dynamics of a tumor{immune system with chemotherapy and immunotherapy and quadratic optimal control. Differential Equations And Dynamical Systems. 24, 149-171, 2016
  • Rodrigues, D., Mancera, P., Carvalho, T., Gonccalves, L.: A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia. Applied Mathematics And Computation. 349, 118-133, 2019
  • Hellal, H., Elabsy, H., Elkaranshawy, H.: Mathematical Model for Combined Radiotherapy and Chemotherapy that Fits with Experimental Data. Journal Of Physics: Conference Series. 2287, 012013, 2022
  • Bekker, R., Kim, S., Pilon-Thomas, S., Enderling, H.: Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system. Neoplasia. 28, 100796, 2022
  • Butuc, I., Mirestean, C., Iancu, D.: A nonlinear model in the dynamics of tumourimmune system combined with radiotherapy. UPB Sci. Bull., Ser. A. 81, 311-322, 2019
  • Pinho, S., Bacelar, F., Andrade, R., Freedman, H.: A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy. Nonlinear Analysis: Real World Applications. 14, 815-828, 2013
  • Esen,  O., Cetin, E., Esen, S.: A mathematical immunochemoradiotherapy model: A multiobjective approach. Nonlinear Analysis: Real World Applications. 9, 511-517, 2008
  • Kuznetsov, M., Kolobov, A.: Algorithm of optimization of fractionated radiotherapy within its combination with antiangiogenic therapy by means of mathematical modeling. ITM Web Of Conferences. 31, 02001 ,2020
  • Kuznetsov, M., Gubernov, V., Kolobov, A.: Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling. Russian Journal Of Numerical Analysis And Mathematical Modelling. 33, 225-242, 2018
  • Hutchinson, L., Mueller, H., Gaffney, E., Maini, P., Wagg, J., Phipps, A., Boetsch, C., Byrne, H., Ribba, B.: Modeling longitudinal preclinical tumor size data to identify transient dynamics in tumor response to antiangiogenic drugs. CPT: Pharmacometrics & Systems Pharmacology. 5, 636-645, 2016
  • Rosch, K., Scholz, M., Hasenclever, D.: Modeling combined chemo-and immunotherapy of high-grade non-Hodgkin lymphoma. Leukemia & Lymphoma. 57, 1697-1708, 2016
  • Yang, J., Tang, S., Cheke, R.: Modelling pulsed immunotherapy of tumour{immune interaction. Mathematics And Computers In Simulation. 109, 92-112, 2015
  • Saleem, M., Farman, M., Ahmad, A., Meraj, M. 31.: Mathematical model based assessment of the cancer control by chemo-immunotherapy. Pure And Applied Biology (PAB). 7, 678-683, 2018
  • Mousta d, A.: Set-valued analysis of anti-angiogenic therapy and radiotherapy. Mathematical Modelling And Numerical Simulation With Applications. 2, 187-196, 2022
  • Kassara, K., Mousta d, A.: Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method. Mathematical Biosciences. 231, 135-143, 2011
  • Mousta d, A.: General anti-angiogenic therapy protocols with chemotherapy. International Journal Of Mathematical Modelling & Computations. 11, 2021
  • Mousta d, A.: Feedback protocols for anti-angiogenic therapy in the treatment of cancer tumors by chemotherapy. International Journal on Optimization and Applications. 2, 17-24, 2022
  • Mousta d, A.: General Chemotherapy Protocols. Journal Of Applied Dynamic Systems And Control. 4, 18-25, 2021
  • Dehingia, K., Sarmah, H., Hosseini, K., Sadri, K., Salahshour, S., Park, C.: An optimal control problem of immuno-chemotherapy in presence of gene therapy. AIMS Mathematics. 6, 11530-11549, 2021
  • Piretto, E., Delitala, M., Ferraro, M.: Combination therapies and intra-tumoral competition: Insights from mathematical modeling. Journal Of Theoretical Biology. 446, 149-159, 2018
  • Abdeljalil, S., Essid, A., Aouadi, S.: Analysis of a tumor growth model with a nonlocal boundary condition. ArXiv Preprint ArXiv:2205.12167, 2022
  • Roy, S., Pal, S.: Optimal personalized therapies in colon-cancer induced immune response using a Fokker-Planck framework. ArXiv Preprint ArXiv:2209.03812, 2022
  • Malinzi, J., Eladdadi, A., Sibanda, P.: Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment. Journal Of Biological Dynamics. 11, 244-274, 2017
  • Nono, M., Ngouonkadi, E., Bowong, S., Fotsin, H.: Spatiotemporal dynamics and optimal control of glioma virotherapy enhanced by MEK Inhibitors. Results In Control And Optimization. 7, 100101, 2022
  • Pomeroy, A., Schmidt, E., Sorger, P., Palmer, A.: Drug independence and the curability of cancer by combination chemotherapy. Trends In Cancer, 2022
  • Abaid Ur Rehman, M., Ahmad, J., Hassan, A., Awrejcewicz, J., Pawlowski, W., Karamti, H., Alharbi, F.: The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease. Symmetry. 14, 1694, 2022
  • Panwar, V., Uduman, P.: Existence a nd Uniqueness of Solutions for Mixed Immunotherapy and Chemotherapy Cancer Treatment Fractional Model with Caputo- Fabrizio Derivative. Progress In Fractional Differentiation And Applications An International Journal. 8, 243-251, 2022
  • Farayolaa, M., Sha ea, S., Siama, F., Mahmudb, R., Ajadic, S.: Mathematical modeling of cancer treatments with fractional derivatives: An Overview. Malaysian Journal Of Fundamental And Applied Sciences. 17, 389-401, 2021
  • Baleanu, D., Jajarmi, A., Sajjadi, S., Mozyrska, D.: A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos: An Interdisciplinary Journal Of Nonlinear Science. 29, 083127 ,2019
  • Yildiz, T., Arshad, S., Baleanu, D.: Optimal chemotherapy and immunotherapy schedules for a cancer-obesity model with Caputo time fractional derivative. ArXiv Preprint ArXiv:1804.06259, 2018
  • Sweilam, N., Rihan, F., Seham, A.: A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies. Discrete & Continuous Dynamical Systems-S. 13, 2403, 2020
  • Erjaee, G., Ostadzad, M., Amanpour, S., Lankarani, K.: Dynamical analysis of the interaction between effector immune and cancer cells and optimal control of chemotherapy. Nonlinear Dynamics, Psychology, And Life Sciences. 17, 449-463, 2013
  • Shamsaraa, E., Esmailyb, H., Bahrampourc, A.: Mathematical Model of Optimal Chemotherapy and Oncolytic Virotherapy. Filomat. 34, 5195-5206, 2020
  • Rihan, F., Lakshmanan, S., Maurer, H.: Optimal control of tumour-immune model with time-delay and immuno-chemotherapy. Applied Mathematics And Computation. 353, 147-165, 2019
  • Das, P., Das, S., Upadhyay, R., Das, P.: Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach. Chaos, Solitons & Fractals. 136, 109806, 2020
  • Moussa, K., Fiacchini, M., Alamir, M.: Probabilistically certi ed region of attraction of a tumor growth model with combined chemo-and immunotherapy. International Journal Of Robust And Nonlinear Control. 2022
  • Deepak, K., Sanjeev, K.: A mathematical model of radioimmunotherapy for tumor treatment. African Journal Of Mathematics And Computer Science Research. 3, 101-106, 2010
  • Kok, H., Rhoon, G., Herrera, T., Overgaard, J., Crezee, J.: Biological modeling in thermoradiotherapy: present status and ongoing developments toward routine clinical use. International Journal Of Hyperthermia. 39, 1126-1140, 2022
  • Ahmadi, E., Zarei, J., Razavi-Far, R., Saif, M.: A dual approach for positive T-S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy. Biomedical Signal Processing And Control. 58, 101822, 2020
  • Roguia, S., Mohamed, N.: An optimized rbf-neural network for breast cancer classication. International Journal Of Informatics And Applied Mathematics. 1, 24-34, 2019
  • Engeland, C., Heidbuechel, J., Araujo, R., Jenner, A.: Improving immunovirotherapies: the intersection of mathematical modelling and experiments. ImmunoInformatics, 100011, 2022
  • Bunonyo, K., Ebiwareme, L.: Tumor growth mathematical modeling and application of chemo-immunotherapy and radiotherapy treatments. Int J Stat Appl Math. 7(2), 123-132, 2022
  • Aubin, J.P.: Viability Theory. Modern Birkhauser Classics, Birkhauser Boston. 2009
  • Grimes, W., Achache, M.: An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. International Journal Of Informatics And Applied Mathematics. 4, 53-59, 2021

Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis

Year 2023, Volume: 6 Issue: 1, 40 - 56, 16.06.2023
https://doi.org/10.53508/ijiam.1211906

Abstract

In this paper we set-valued analyze the problem of asymptotic stabilizing the tumor size. A mathematical model of exponential tumor growing caused by carcinogenic substance is considered, with chemotherapy, immunotherapy, and radiotherapy effects. We control the model to be viable in therapeutic domains, and reverse the exponential growing of the tumor size. The obtained controls derive from the derivative cone of therapeutic domains as solution of minimizing problem.

References

  • El Haout, S., Fatani, M., Farha, N., AlSawaftah, N., Mortula, M., Husseini, G.: Modeling the Effects of Chemotherapy and Immunotherapy on Tumor Growth. Journal Of Biomedical Nanotechnology. 17, 2505-2518, 2021
  • Pratap, J.: An optimal control strategy for mathematically modeling cancer combination therapy. ArXiv Preprint ArXiv:2101.12120, 2021
  • Nave, O.: A mathematical model for treatment using chemo-immunotherapy. Heliyon. 8, e09288, 2022
  • Unni, P., Seshaiyer, P.: Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions. Computational And Mathematical Methods In Medicine, 2019
  • Sharma, S., Samanta, G.: Analysis of the dynamics of a tumor{immune system with chemotherapy and immunotherapy and quadratic optimal control. Differential Equations And Dynamical Systems. 24, 149-171, 2016
  • Rodrigues, D., Mancera, P., Carvalho, T., Gonccalves, L.: A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia. Applied Mathematics And Computation. 349, 118-133, 2019
  • Hellal, H., Elabsy, H., Elkaranshawy, H.: Mathematical Model for Combined Radiotherapy and Chemotherapy that Fits with Experimental Data. Journal Of Physics: Conference Series. 2287, 012013, 2022
  • Bekker, R., Kim, S., Pilon-Thomas, S., Enderling, H.: Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system. Neoplasia. 28, 100796, 2022
  • Butuc, I., Mirestean, C., Iancu, D.: A nonlinear model in the dynamics of tumourimmune system combined with radiotherapy. UPB Sci. Bull., Ser. A. 81, 311-322, 2019
  • Pinho, S., Bacelar, F., Andrade, R., Freedman, H.: A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy. Nonlinear Analysis: Real World Applications. 14, 815-828, 2013
  • Esen,  O., Cetin, E., Esen, S.: A mathematical immunochemoradiotherapy model: A multiobjective approach. Nonlinear Analysis: Real World Applications. 9, 511-517, 2008
  • Kuznetsov, M., Kolobov, A.: Algorithm of optimization of fractionated radiotherapy within its combination with antiangiogenic therapy by means of mathematical modeling. ITM Web Of Conferences. 31, 02001 ,2020
  • Kuznetsov, M., Gubernov, V., Kolobov, A.: Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling. Russian Journal Of Numerical Analysis And Mathematical Modelling. 33, 225-242, 2018
  • Hutchinson, L., Mueller, H., Gaffney, E., Maini, P., Wagg, J., Phipps, A., Boetsch, C., Byrne, H., Ribba, B.: Modeling longitudinal preclinical tumor size data to identify transient dynamics in tumor response to antiangiogenic drugs. CPT: Pharmacometrics & Systems Pharmacology. 5, 636-645, 2016
  • Rosch, K., Scholz, M., Hasenclever, D.: Modeling combined chemo-and immunotherapy of high-grade non-Hodgkin lymphoma. Leukemia & Lymphoma. 57, 1697-1708, 2016
  • Yang, J., Tang, S., Cheke, R.: Modelling pulsed immunotherapy of tumour{immune interaction. Mathematics And Computers In Simulation. 109, 92-112, 2015
  • Saleem, M., Farman, M., Ahmad, A., Meraj, M. 31.: Mathematical model based assessment of the cancer control by chemo-immunotherapy. Pure And Applied Biology (PAB). 7, 678-683, 2018
  • Mousta d, A.: Set-valued analysis of anti-angiogenic therapy and radiotherapy. Mathematical Modelling And Numerical Simulation With Applications. 2, 187-196, 2022
  • Kassara, K., Mousta d, A.: Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method. Mathematical Biosciences. 231, 135-143, 2011
  • Mousta d, A.: General anti-angiogenic therapy protocols with chemotherapy. International Journal Of Mathematical Modelling & Computations. 11, 2021
  • Mousta d, A.: Feedback protocols for anti-angiogenic therapy in the treatment of cancer tumors by chemotherapy. International Journal on Optimization and Applications. 2, 17-24, 2022
  • Mousta d, A.: General Chemotherapy Protocols. Journal Of Applied Dynamic Systems And Control. 4, 18-25, 2021
  • Dehingia, K., Sarmah, H., Hosseini, K., Sadri, K., Salahshour, S., Park, C.: An optimal control problem of immuno-chemotherapy in presence of gene therapy. AIMS Mathematics. 6, 11530-11549, 2021
  • Piretto, E., Delitala, M., Ferraro, M.: Combination therapies and intra-tumoral competition: Insights from mathematical modeling. Journal Of Theoretical Biology. 446, 149-159, 2018
  • Abdeljalil, S., Essid, A., Aouadi, S.: Analysis of a tumor growth model with a nonlocal boundary condition. ArXiv Preprint ArXiv:2205.12167, 2022
  • Roy, S., Pal, S.: Optimal personalized therapies in colon-cancer induced immune response using a Fokker-Planck framework. ArXiv Preprint ArXiv:2209.03812, 2022
  • Malinzi, J., Eladdadi, A., Sibanda, P.: Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment. Journal Of Biological Dynamics. 11, 244-274, 2017
  • Nono, M., Ngouonkadi, E., Bowong, S., Fotsin, H.: Spatiotemporal dynamics and optimal control of glioma virotherapy enhanced by MEK Inhibitors. Results In Control And Optimization. 7, 100101, 2022
  • Pomeroy, A., Schmidt, E., Sorger, P., Palmer, A.: Drug independence and the curability of cancer by combination chemotherapy. Trends In Cancer, 2022
  • Abaid Ur Rehman, M., Ahmad, J., Hassan, A., Awrejcewicz, J., Pawlowski, W., Karamti, H., Alharbi, F.: The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease. Symmetry. 14, 1694, 2022
  • Panwar, V., Uduman, P.: Existence a nd Uniqueness of Solutions for Mixed Immunotherapy and Chemotherapy Cancer Treatment Fractional Model with Caputo- Fabrizio Derivative. Progress In Fractional Differentiation And Applications An International Journal. 8, 243-251, 2022
  • Farayolaa, M., Sha ea, S., Siama, F., Mahmudb, R., Ajadic, S.: Mathematical modeling of cancer treatments with fractional derivatives: An Overview. Malaysian Journal Of Fundamental And Applied Sciences. 17, 389-401, 2021
  • Baleanu, D., Jajarmi, A., Sajjadi, S., Mozyrska, D.: A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos: An Interdisciplinary Journal Of Nonlinear Science. 29, 083127 ,2019
  • Yildiz, T., Arshad, S., Baleanu, D.: Optimal chemotherapy and immunotherapy schedules for a cancer-obesity model with Caputo time fractional derivative. ArXiv Preprint ArXiv:1804.06259, 2018
  • Sweilam, N., Rihan, F., Seham, A.: A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies. Discrete & Continuous Dynamical Systems-S. 13, 2403, 2020
  • Erjaee, G., Ostadzad, M., Amanpour, S., Lankarani, K.: Dynamical analysis of the interaction between effector immune and cancer cells and optimal control of chemotherapy. Nonlinear Dynamics, Psychology, And Life Sciences. 17, 449-463, 2013
  • Shamsaraa, E., Esmailyb, H., Bahrampourc, A.: Mathematical Model of Optimal Chemotherapy and Oncolytic Virotherapy. Filomat. 34, 5195-5206, 2020
  • Rihan, F., Lakshmanan, S., Maurer, H.: Optimal control of tumour-immune model with time-delay and immuno-chemotherapy. Applied Mathematics And Computation. 353, 147-165, 2019
  • Das, P., Das, S., Upadhyay, R., Das, P.: Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach. Chaos, Solitons & Fractals. 136, 109806, 2020
  • Moussa, K., Fiacchini, M., Alamir, M.: Probabilistically certi ed region of attraction of a tumor growth model with combined chemo-and immunotherapy. International Journal Of Robust And Nonlinear Control. 2022
  • Deepak, K., Sanjeev, K.: A mathematical model of radioimmunotherapy for tumor treatment. African Journal Of Mathematics And Computer Science Research. 3, 101-106, 2010
  • Kok, H., Rhoon, G., Herrera, T., Overgaard, J., Crezee, J.: Biological modeling in thermoradiotherapy: present status and ongoing developments toward routine clinical use. International Journal Of Hyperthermia. 39, 1126-1140, 2022
  • Ahmadi, E., Zarei, J., Razavi-Far, R., Saif, M.: A dual approach for positive T-S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy. Biomedical Signal Processing And Control. 58, 101822, 2020
  • Roguia, S., Mohamed, N.: An optimized rbf-neural network for breast cancer classication. International Journal Of Informatics And Applied Mathematics. 1, 24-34, 2019
  • Engeland, C., Heidbuechel, J., Araujo, R., Jenner, A.: Improving immunovirotherapies: the intersection of mathematical modelling and experiments. ImmunoInformatics, 100011, 2022
  • Bunonyo, K., Ebiwareme, L.: Tumor growth mathematical modeling and application of chemo-immunotherapy and radiotherapy treatments. Int J Stat Appl Math. 7(2), 123-132, 2022
  • Aubin, J.P.: Viability Theory. Modern Birkhauser Classics, Birkhauser Boston. 2009
  • Grimes, W., Achache, M.: An Infeasible Interior-point Algorithm for Monotone Linear Complementarity Problems. International Journal Of Informatics And Applied Mathematics. 4, 53-59, 2021
There are 48 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Articles
Authors

Amine Moustafid

Early Pub Date June 3, 2023
Publication Date June 16, 2023
Acceptance Date April 23, 2023
Published in Issue Year 2023 Volume: 6 Issue: 1

Cite

APA Moustafid, A. (2023). Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis. International Journal of Informatics and Applied Mathematics, 6(1), 40-56. https://doi.org/10.53508/ijiam.1211906
AMA Moustafid A. Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis. IJIAM. June 2023;6(1):40-56. doi:10.53508/ijiam.1211906
Chicago Moustafid, Amine. “Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis”. International Journal of Informatics and Applied Mathematics 6, no. 1 (June 2023): 40-56. https://doi.org/10.53508/ijiam.1211906.
EndNote Moustafid A (June 1, 2023) Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis. International Journal of Informatics and Applied Mathematics 6 1 40–56.
IEEE A. Moustafid, “Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis”, IJIAM, vol. 6, no. 1, pp. 40–56, 2023, doi: 10.53508/ijiam.1211906.
ISNAD Moustafid, Amine. “Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis”. International Journal of Informatics and Applied Mathematics 6/1 (June 2023), 40-56. https://doi.org/10.53508/ijiam.1211906.
JAMA Moustafid A. Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis. IJIAM. 2023;6:40–56.
MLA Moustafid, Amine. “Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis”. International Journal of Informatics and Applied Mathematics, vol. 6, no. 1, 2023, pp. 40-56, doi:10.53508/ijiam.1211906.
Vancouver Moustafid A. Viability Control of Chemo-Immunotherapy and Radiotherapy by Set-Valued Analysis. IJIAM. 2023;6(1):40-56.

International Journal of Informatics and Applied Mathematics