A new mathematical model approach on the oncolytic virotherapy potency

Volume 36, Issue 1, pp 99--120 https://dx.doi.org/10.22436/jmcs.036.01.07

Publication Date: June 26, 2024 Submission Date: April 06, 2024 Revision Date: May 13, 2024 Accteptance Date: May 25, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 79 Downloads
• 314 Views

Authors

A‎. ‎T‎. ‎ Alshammari - Department of Mathematical Sciences‎, ‎Faculty of Science, ‎Universiti Teknologi Malaysia, Johor Bahru 81310, ‎Johor, ‎Malaysia. - Department of Mathematics, Faculty of Science, University of Hafr Al Batin, Hafr Al Batin, Saudi Arabia. ‎N‎. ‎ Maan - Department of Mathematical Sciences‎, ‎Faculty of Science, ‎Universiti Teknologi Malaysia, ‎Johor Bahru 81310, ‎Johor, ‎Malaysia. M. A‎. ‎M‎. ‎ Abdelaziz - School of Quantitative Sciences‎, ‎College of Arts \(\&\) Sciences, ‎Universiti Utara Malaysia, Kedah, Malaysia. - Department of Mathematics‎, ‎Faculty of Arts and Sciences, Najran University, Najran, Saudi Arabia.

Abstract

‎In recent times‎, ‎there has been an increasing focus on investigating the therapeutic capacity of virus particles in the management of cancer‎. ‎This paper introduces a novel discrete-time mathematical model with fractional-order of oncolytic virotherapy‎. ‎The model captures the complex behavior of how cancer cells and virus particles interact‎, ‎aiming to elucidate the process of infecting and eliminating cancer cells in the absence of immune involvement‎. ‎To evaluate the efficacy of cancer-targeting virus treatment‎, ‎we perform an in-depth analysis of both the local stability and the bifurcation trends observed in our framework‎. ‎By selecting appropriate bifurcation parameters‎, ‎we verify the occurrence of codimension one bifurcations‎, ‎for instance‎, ‎fold‎, ‎flip as well as Neimark-Sacker (N-S)‎, ‎as well as codimension-two flip-N-S bifurcations‎. ‎ The identification of these bifurcation types is established by deriving necessary and sufficient conditions using algebraic criterion methods‎. ‎In these criteria‎, ‎the reliance does not lie in the attributes of the eigenvalue coefficients from the characteristic equation of the Jacobian matrix but rather on the coefficients of the Jacobian matrix's characteristic equation itself‎. ‎Consequently‎, ‎we have semi-algebraic systems comprising equations‎, ‎inequalities‎, ‎and inequalities‎. ‎This algebraic methodology provides appropriate conditions for both codimension one as well as codimension-two bifurcations in high-dimensional maps‎. ‎Finally‎, ‎numerical simulations were conducted to validate our theoretical findings‎. ‎Our study concludes that the correlated increase between cancer cell proliferation and the therapeutic virus indeed resulted in the anticipated infection within the cancer cells‎. ‎While complete eradication of cancer cells using viral therapy alone is not impossible‎, ‎it requires specific conditions‎.

Share and Cite

Keywords

• Virotherapy cancer treatment
• calculus involving fractional orders
• model in discrete time
• equilibrium stability
• bifurcations
• chaos

MSC

•  37N25
•  92C50‎
•  35Q92

References

• [1] M. A. M. Abdelaziz, A. I. Ismail, F. A. Abdullah, M. H. Mohd, Bifurcations and chaos in a discrete SI epidemic model with fractional order, Adv. Difference Equ., 2018 (2018), 1–19
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] M. A. M. Abdelaziz, A. I. Ismail, F. A. Abdullah, M. H. Mohd, Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination, Chaos Solitons Fractals, 140 (2020), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] M. J. Ailia, S. Y. Yoo, In vivo oncolytic virotherapy in murine models of hepatocellular carcinoma: a systematic review, Vaccines, 10 (2022), 1–16
  • View Article
  • Google Scholar


• [4] A. H. Alblowy, N. Maan, S. A. Alharbi, Role of glucose risk factors on human breast cancer: A nonlinear dynamical model evaluation, Mathematics, 10 (2022), 1–20
  • View Article
  • Google Scholar


• [5] A. A. Al-Zaher, R. Moreno, C. A. Fajardo, M. Arias-Badia, M. Farrera, J. de Sostoa, L. A. Rojas, R. Alemany, Evidence of anti-tumoral efficacy in an immune competent setting with an irgd-modified hyaluronidase-armed oncolytic adenovirus, Mol. Ther., 8 (2018), 62–70
  • View Article
  • Google Scholar


• [6] S. E. Berkey, S. H. Thorne, D. L. Bartlett, Oncolytic virotherapy and the tumor microenvironment, In: Tumor Immune Microenvironment in Cancer Progression and Cancer Therapy, Adv. Exp. Med. Biol., Springer, Cham, (2017), 157–172
  • View Article
  • Google Scholar


• [7] H. Boutayeb, S. Bidah, O. Zakary, M. Rachik, A new simple epidemic discrete-time model describing the dissemination of information with optimal control strategy, Discrete Dyn. Nat. Soc., 2020 (2020), 11 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] W. M. Chan, G. McFadden, Oncolytic poxviruses, Annu. Rev. Virol., 1 (2014), 191–214
  • View Article
  • Google Scholar


• [9] B. S. Chhikara, K. Parang, Global cancer statistics 2022: the trends projection analysis, Chem. Biol. Lett., 10 (2023), 1–16
  • View Article
  • Google Scholar


• [10] A. El-Sayed, S. Salman, On a discretization process of fractional-order riccati differential equation, J. Fract. Calc. Appl., 4 (2013), 251–259
  • View Article
  • Google Scholar
  • MATH


• [11] M. Farman, A. Akg¨ ul, A. Ahmad, S. Imtiaz, Analysis and dynamical behavior of fractional-order cancer model with vaccine strategy, Math. Methods Appl. Sci., 43 (2020), 4871–4882
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] A. C. Filley, M. Dey, Immune system, friend or foe of oncolytic virotherapy?, Front. Oncol., 7 (2017), 1–17
  • View Article
  • Google Scholar


• [13] A. L. Jenner, A. C. F. Coster, P. S. Kim, Treating cancerous cells with viruses: insights from aminimal model for oncolytic virotherapy, Lett. Biomath., 5 (2018), S117–S136
  • View Article
  • Google Scholar


• [14] P. Kumar, V. S. Erturk, A. Yusuf, S. Kumar, Fractional time-delay mathematical modeling of oncolytic virotherapy, Chaos Solitons Fractals, 150 (2021), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [15] X. Li, C. Mou, W. Niu, D.Wang, Stability analysis for discrete biological models using algebraic methods, Math. Comput. Sci., 5 (2011), 247–262
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] A. C. J. Luo, Regularity and complexity in dynamical systems, Springer, New York (2012)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] A. M. Malfitano, S. Di Somma, N. Prevete, G. Portella, Virotherapy as a potential therapeutic approach for the treatment of aggressive thyroid cancer, Cancers, 11 (2019), 1–21
  • View Article
  • Google Scholar


• [18] J. Malinzi, A mathematical model for oncolytic virus spread using the telegraph equation, Commun. Nonlinear Sci. Numer. Simul., 102 (2021), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] C. E. Miller, The endometrioma treatment paradigm when fertility is desired: a systematic review, J. Minim. Invasive Gynecol., 28 (2021), 575–586
  • View Article
  • Google Scholar


• [20] K. D. Miller, L. Nogueira, A. B. Mariotto, J. H. Rowland, K. R. Yabroff, C. M. Alfano, A. Jemal, J. L. Kramer, R. L. Siegel, Cancer treatment and survivorship statistics, 2019, CA Cancer J. Clin., 69 (2019), 363–685
  • View Article
  • Google Scholar


• [21] H. Murphy, H. Jaafari, H. M. Dobrovolny, Differences in predictions of ode models of tumor growth: a cautionary example, BMC Cancer, 16 (2016), 1–10
  • View Article
  • Google Scholar


• [22] W. Niu, J. Shi, C. Mou, Analysis of codimension 2 bifurcations for high-dimensional discrete systems using symbolic computation methods, Appl. Math. Comput., 273 (2016), 934–947
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [23] E. Ratajczyk, U. Ledzewicz, H. Sch¨attler, Optimal control for a mathematical model of glioma treatment with oncolytic therapy and TNF- inhibitors, J. Optim. Theory Appl., 176 (2018), 456–477
  • View Article
  • MathSciNet
  • Google Scholar


• [24] L. A. Santry, J. P. van Vloten, J. P. Knapp, K. Matuszewska, T. M. McAusland, J. A. Minott, R. C. Mould, A. A. Stegelmeier, P. P. Major, S. K. Wootton, J. J. Petrik, B. W. Bridle, Tumour vasculature: friend or foe of oncolytic viruses?, Cytokine Growth Factor. Rev., 56 (2020), 69–82
  • View Article
  • Google Scholar


• [25] E. Shirbhate, R. Veerasamy, S. H. S. Boddu, A. K. Tiwari, H. Rajak, Histone deacetylase inhibitor-based oncolytic virotherapy: A promising strategy for cancer treatment, Drug Discov. Today, 27 (2022), 1689–1697
  • View Article
  • Google Scholar


• [26] J. d. Sostoa, V. Dutoit, D. Migliorini, Oncolytic viruses as a platform for the treatment of malignant brain tumors, Int. J. Mol. Sci., 21 (2020), 1–21
  • View Article
  • Google Scholar


• [27] Y. R. Suryawanshi, A. J. Schulze, Oncolytic viruses for malignant glioma: on the verge of success?, Viruses, 13 (2021), 1–25
  • View Article
  • Google Scholar


• [28] C. A. Valentim, J. A. Rabi, S. A. David, Fractional mathematical oncology: On the potential of non-integer order calculus applied to interdisciplinary models, Biosystems, 204 (2021),
  • View Article
  • Google Scholar


• [29] C. A. Valentim Jr, N. A. Oliveira, J. A. Rabi, S. A. David, Can fractional calculus help improve tumor growth models?, J. Comput. Appl. Math., 379 (2020), 15 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [30] P. Van den Driessche, J. Watmough, Further notes on the basic reproduction number, Springer, Berlin, 1945 (2008), 159–178
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [31] B. D. Weinberg, J. Gao, Polymer implants for intratumoral drug delivery and cancer therapy, CRC Press, (2020)
  • View Article
  • Google Scholar


• [32] G. Wen, Criterion to identify Hopf bifurcations in maps of arbitrary dimension, Phys. Rev. E (3), 72 (2005), 4 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [33] G. Wen, S. Chen, Q. Jin, A new criterion of period-doubling bifurcation in maps and its application to an inertial impact shaker, J. Sound Vib., 311 (2008), 212–223
  • View Article
  • Google Scholar


• [34] D. Wodarz, Gene therapy for killing p53-negative cancer cells: use of replicating versus nonreplicating agents, Hum. Gene Ther., 14 (2003), 153–159
  • View Article
  • Google Scholar


• [35] T. Yamada, Y. Hamano, N. Hasegawa, E. Seo, K. Fukuda, K. K Yokoyama, I. Hyodo, M. Abei, Oncolytic virotherapy and gene therapy strategies for hepatobiliary cancers, Curr. Cancer Drug Targets, 18 (2008), 188–201
  • View Article
  • Google Scholar


• [36] S. Yao, New bifurcation critical criterion of flip-Neimark-Sacker bifurcations for two-parameterized family of n-dimensional discrete systems, Discrete Dyn. Nat. Soc., 2012 (2012), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [37] Y. Zhou, J. W. He, A cauchy problem for fractional evolution equations with hilfer’s fractional derivative on semiinfinite interval, Fract. Calc. Appl. Anal., 25 (2022), 924–961
  • View Article
  • Google Scholar