Mathematical Modelling Simulation of Oncolytic Virotherapy Cancer Treatment
DOI:
https://doi.org/10.47611/jsrhs.v13i4.7531Keywords:
Oncolytic Virotherapy, Cancer Treatment, Hopf Bifurcation, Differential Equations, Burst Size, Tumour LoadAbstract
Oncolytic virotherapy is a cancer treatment that uses replicating viruses to target and kill tumour cells. The interaction between tumour cells and an oncolytic virus can be represented in a mathematical model. In this paper we study the development of some mathematical models and their dynamics. We study the conclusions of various approaches to the modelling, including a system of ordinary differential equations, the dynamical system’s theory, and a predatory-prey model. The study analyses thresholds that enable us to identify solutions of a virus-cell interaction function. We run Hopf bifurcation to classify stable equilibrium points in the function. We also propose a mathematical model on oncolytic virotherapy incorporating multiple cell populations and free viruses. Optimal viral burst sizes to reduce tumour load in the quickest time are obtained. Burst sizes around 25 were found to be optimal, and 3 viral drugs, including a modified HSV and an adenovirus ONYX-015, were presented as the most effective treatments.
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Abu-Rqayiq, A. (2021, April 23). Mathematical Modeling and Dynamics of Oncolytic Virotherapy. Retrieved from https://www.intechopen.com/chapters/76116. doi: 10.5772/intechopen.96963
Wang, Z., Guo, S., & Smith, H. (2019, March 6). A mathematical model of oncolytic virotherapy with time delay[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 1836-1860. Retrieved from https://www.aimspress.com/article/id/3453. doi: 10.3934/mbe.2019089
Cancer Survival Statistics (2023, September 27). Cancer Research UK. Retrieved from https://www.cancerresearchuk.org/health-professional/cancer-statistics/survival#:~:text=Many%20of%20the%20most%20commonly,more%20(2010%2D11)
Wodarz, D. (2003, January 20). Gene Therapy for Killing p53-Negative Cancer Cells: Use of Replicating Versus Nonreplicating Agents. Human Gene Therapy, 2003, 14(2): 153-159. Retrieved from https://www.liebertpub.com/doi/10.1089/104303403321070847. doi: 10.1089/104303403321070847
Norman, K.L, Farassati, F., & Lee, P.W. (2001, June-September). Oncolytic viruses and cancer therapy. Retrieved from https://pubmed.ncbi.nlm.nih.gov/11325607/
Wein, L.M., Wu, J.T., & Kirn, D.H. (2003, March 15). Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: implications for virus design and delivery. Retrieved from https://pubmed.ncbi.nlm.nih.gov/12649193/
Novozhilov, A.S., Berezovskaya, F.S., Koonin, E.V., & Karev, G.P. (2006, February 17). Mathematical modeling of tumor therapy with oncolytic viruses: Regimes with complete tumor elimination within the framework of deterministic models. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1403749/. doi: 10.1186/1745-6150-1-6
Friedman, A., & Kao, C-Y. (2014). Mathematical Modeling of Biological Processes. Springer International Publishing Switzerland.
Friedman, A., & Tao, Y (2003, November). Analysis of a Model of a Virus that Replicates Selectively in Tumor Cells. Journal of Mathematical Biology. Retrieved from https://pubmed.ncbi.nlm.nih.gov/14605856/
Delbrück, M. (1945). The Burst Size Distribution in the Growth of Bacterial Viruses (Bacteriophages). Retrieved from https://journals.asm.org/doi/pdf/10.1128/jb.50.2.131-135.1945
Koelle, D.M., & Wald, A. (2000). Herpes simplex virus: the importance of asymptomatic shedding. Journal of Antimicrobial Chemotherapy, 2000, 45: Topic T3, 1-8. Retrieved from https://watermark.silverchair.com/
Tian, J.P. (2011). The replicability of oncolytic virus: defining conditions in tumor virotherapy. Retrieved from https://pubmed.ncbi.nlm.nih.gov/21675814/
J Bone Oncol, 2019, 14. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6348933/. doi: 10.1016/j.jbo.2018.100211
Ries, S., & Korn, W.M (2002). ONYX-015: Mechanisms of action and clinical potential of a replication-selective adenovirus. British Journal of Cancer, 86: 5-11. Retrieved from https://www.researchgate.net/publication/11504842_ONYX-015_Mechanisms_of_action_and_clinical_potential_of_a_replication-selective_adenovirus
Equilibrium Solutions (n.d.). Study Pug. Retrieved from https://www.studypug.com/differential-equations-help/equilibrium-solutions#:~:text=If%20nearby%20solutions%20to%20the,have%20an%20unstable%20equilibrium%20point
Heijden, G. (n.d.). Hopf Bifurcation – UCL. Retrieved from https://www.ucl.ac.uk/~ucesgvd/hopf.pdf
Jacobian Matrix and Determinant (Definition and Formula) (2019, December 9). BYJUS. Retrieved from https://byjus.com/maths/jacobian/
Law of Mass Action – Definition, Application & Equation with Statement (2022, August 19). BYJUS. Retrieved from https://byjus.com/chemistry/law-of-mass-action-or-law-of-chemical-equilibrium/
Khan, F.A., Akhtar, S.S., & Sheikh, M.K. (2005, January). Cancer Treatment – Objectives and Quality of Life Issues[J]. Malays J Med Sci, 2005, 12(1): 3-5. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3349406/
Kumar, P., Erturk, V.S., Yusuf, A., & Kumar, S. (2021, June 19). Fractional time-delay mathematical modeling of Oncolytic Virotherapy[J]. Chaos, Solitons & Fractals, 2021, 150. Retrieved from https://www.sciencedirect.com/science/article/abs/pii/S096007792100477X. doi: 10.1016/j.chaos.2021.111123
What is Cancer (n.d.). National Cancer Institute. Retrieved from https://www.cancer.gov/about-cancer/understanding/what-is-cancer#:~:text=Cancer%20is%20a%20disease%20in,up%20of%20trillions%20of%20cells
What is Parallel Computing? Definition and FAQs (n.d.). HEAVY.AI. Retrieved from https://www.heavy.ai/technical-glossary/parallel-computing#:~:text=Parallel%20computing%20refers%20to%20the,part%20of%20an%20overall%20algorithm
Zou, C. et al. (2018, December 14). Managements of giant cell tumor within the distal radius: A retrospective study of 58 cases from a single center.
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