Time delay induces a back to back Hopf bifurcation on oncolytic virotherapy.
DOI:
https://doi.org/10.31686/ijier.vol11.iss5.4121Keywords:
computational biology, bifurcation, dynamical system, oncolytic virotherapyAbstract
This study analyzes a basic mathematical model for the dynamic interactions among tumor cells, infected tumor cells and viruses population, focusing on the viral lytic cycle for oncolytic virotherapy. I study the time delay effect of viral infection on tumor cell populations by identifying bifurcation thresholds in both the burst rate and time delay of viral infection in oncolytic virus therapy. Time delay plays an important role in changing the structure of tumor cell populations in a dynamical system. The multi-bifurcation thresholds of the time delay are observed and also dependent on the bursting rate. This study demonstrates a strong relationship between viral burst rates and time delays in population dynamics. The results of this study show that time delay affects oscillation generation and results in back-to-back Hopf bifurcation. This study provides insight into understanding the relationship between the two control parameters, in which tumor cell populations pattern from equilibrium steady-state solutions to periodic solutions and from periodic solutions to equilibrium-state solutions.
Downloads
References
Bajzer, Ž., Carr, T., Josić, K. (2008). Modeling of cancer virotherapy with recombinant measles viruses. Journal of theoretical Biology, 252(1): 109–122. [PubMed: 18316099] DOI: https://doi.org/10.1016/j.jtbi.2008.01.016
Chiocca, E. A. (2002). Oncolytic viruses. Nature Reviews Cancer, 2(12): 938. [PubMed: 12459732] DOI: https://doi.org/10.1038/nrc948
Chiocca, E. A., & Rabkin, S. D. (2014). Oncolytic viruses and their application to cancer immunotherapy, Cancer Immunol Res. 2(4): 295–00. [PubMed: 24764576] DOI: https://doi.org/10.1158/2326-6066.CIR-14-0015
Friedman, A., Tian, J. P., & Fulci, G. (2006). Glioma virotherapy: effects of innate immune suppression and increased viral replication capacity. Cancer research, 66(4): 2314–2319. [PubMed: 16489036] DOI: https://doi.org/10.1158/0008-5472.CAN-05-2661
Harpold, H. L., Alvord, E.C. Jr, & Swanson, K. R. (2007). The evolution of mathematical modeling of glioma proliferation and invasion. J Neuropathol Exp Neurol. 66(1): 1–9. [PubMed: 17204931] DOI: https://doi.org/10.1097/nen.0b013e31802d9000
Kaplan, J. M. (2005). Adenovirus-based cancer gene therapy. Current gene therapy, 5(6): 595–605. [PubMed: 16457649] DOI: https://doi.org/10.2174/156652305774964677
Karev, G. P., Novozhilov, A. S., & Koonin, E.V.(2006). Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics. Biology direct, 1(1): 30. [PubMed: 17018145] DOI: https://doi.org/10.1186/1745-6150-1-30
Kirn, D. H., & McCormick, F. (1996). Replicating viruses as selective cancer therapeutics. Molecular Medicine Today, 2(12): 519–527. [PubMed: 9015793] DOI: https://doi.org/10.1016/S1357-4310(97)81456-6
Lawler, S. E., Speranza, M. C., & Cho, C. F. (2017). Oncolytic viruses in cancer treatment: a review. JAMAoncology, 3(6): 841–849. [PubMed: 27441411] DOI: https://doi.org/10.1001/jamaoncol.2016.2064
Martuza, R. L., Malick, A., & Markert, J. M. (1991) Experimental therapy of human glioma by means of a genetically engineered virus mutant. Science, 252(5007): 854–856. [PubMed: 1851332] DOI: https://doi.org/10.1126/science.1851332
Maroun, J., Muoz-Ala, M., Ammayappan, A., Schulze, A., Peng, K. W., & Russell, S. (2017). Designing and building oncolytic viruses, Future Virol. 12(4), 193–13. [PubMed: 29387140] DOI: https://doi.org/10.2217/fvl-2016-0129
Mok, W., Stylianopoulos, T., Boucher, Y., & Jain, R. K. (2009). Mathematical modeling of herpes simplex virus distribution in solid tumors: implications for cancer gene therapy, Clin Cancer Res., 15(7): 2352–360. [PubMed: 19318482] DOI: https://doi.org/10.1158/1078-0432.CCR-08-2082
Novozhilov, A. S., Berezovskaya, F. S., & Koonin, E. V. (2006). Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models. Biology direct, 1(1): 6. [PubMed: 16542009] DOI: https://doi.org/10.1186/1745-6150-1-6
Roberts, M. S., Lorence, R. M., & Groene, W. S. (2006) Naturally oncolytic viruses. Current opinion in molecular therapeutics, 8(4): 314–321. [PubMed: 16955694]
Wang, Y., Tian, J. P., & Wei, J. (2013). Lytic cycle: a defining process in oncolytic virotherapy. Applied Mathematical Modelling, 37(8): 5962–5978. DOI: https://doi.org/10.1016/j.apm.2012.12.004
Wein, L. M., Wu, J. T., & Kirn, D. H. (2003). Validation and analysis of a mathematical model of a replicationcompetent oncolytic virus for cancer treatment: implications for virus design and delivery. Cancer research, 63(6): 1317–1324. [PubMed: 12649193]
Wodarz, D. (2001). Viruses as antitumor weapons: defining conditions for tumor remission. Cancer research, 61(8): 3501–3507. [PubMed: 11309314]
Wodarz, D., & Komarova, N.(2009). Towards predictive computational models of oncolytic virus therapy: basis for experimental validation and model selection. PloS one, 4(1): e4271. [PubMed: 19180240] DOI: https://doi.org/10.1371/journal.pone.0004271
Wu, J. T., Byrne, H. M., & Kirn, D. H. (2001). Modeling and analysis of a virus that replicates selectively in tumor cells. Bulletin of mathematical biology, 63(4): 731. [PubMed: 11497166] DOI: https://doi.org/10.1006/bulm.2001.0245
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Dong-Hoon Shin
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyrights for articles published in IJIER journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author for more visit Copyright & License.
How to Cite
Accepted 2023-05-03
Published 2023-05-09
