Dynamics of a mathematical model of oncolytic virotherapy with tumor-Virus interaction
Authors
A. Abu-Rqayiq
- Concord University , Athens, WV, 24712, USA.
H. Alayed
- New Mexico State University, Las Cruces, NM, 88001, USA.
Abstract
Virotherapy is a cancer treatment that uses a virus that can target cancer cells to infect, replicate, and destroy them leaving the healthy cells unharmed. Recently, considerable efforts have been made to understand the mechanisms and dynamics of oncolytic virotherapy. In this paper, we study the dynamics of a basic model of oncolytic tumor virotherapy. This model emphasizes the interaction between cancer-infected cells and cancer uninfected cells. To understand some of the consequences of this contact from a mathematical point of view, we study the dynamics behavior of the model and present a qualitative analysis of the equilibria. To illustrate which parameters in the model affect the outcome of virotherapy the most, we determine bifurcation parameters and conduct a sensitivity analysis of the model's parameters. Numerical simulations are conducted to show the validity of our analysis.
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ISRP Style
A. Abu-Rqayiq, H. Alayed, Dynamics of a mathematical model of oncolytic virotherapy with tumor-Virus interaction, Journal of Mathematics and Computer Science, 31 (2023), no. 4, 461--476
AMA Style
Abu-Rqayiq A., Alayed H., Dynamics of a mathematical model of oncolytic virotherapy with tumor-Virus interaction. J Math Comput SCI-JM. (2023); 31(4):461--476
Chicago/Turabian Style
Abu-Rqayiq, A., Alayed, H.. "Dynamics of a mathematical model of oncolytic virotherapy with tumor-Virus interaction." Journal of Mathematics and Computer Science, 31, no. 4 (2023): 461--476
Keywords
- Cancer
- oncolytic virotherapy
- stability
- Lyapunov
- basic reproductive number
MSC
References
-
[1]
A. Abu-Rqayiq, Mathematical Modeling & Dynamics of Oncolytic Virotherapy, In: Advances in Precision Medicine Oncology, Intechopen Publisher, U.K., (2021),
-
[2]
A. Abu-Rqayiq, M. Zannon, On the dynamics of fractional-order oncolytic virotherapy models, J. Math. Comput. Sci., 20 (2020), 79–87
-
[3]
Z. Bajzer, T. Carr, K. Josi´c, S. J. Russell, D. Dingli, Modeling of cancer virotherapy with recombinant measles viruses, J. Theoret. Biol., 252 (2008), 109–122
-
[4]
D. R. Berg, A Flexible Simulator for Oncolytic Viral Therapy, Master Thesis, University of Minnesota ProQuest Dissertations Publishing, (2015)
-
[5]
D. R. Berg, C. P. Offord, I. Kemler, M. K. Ennis, L. Chang, G. Paulik, Z. Bajzer, C. Neuhauser, D. Dingli, In vitro and in silico multidimensional modeling of oncolytic tumor virotherapy dynamics, PLoS Comput. Biol., 15 (2019), 1–18
-
[6]
M. Biesecker, J.-H. Kimn, H. Lu, D. Dingli, Zˇ . Bajzer, Optimization of virotherapy for cancer, Bull. Math. Biol., 72 (2010), 469–489
-
[7]
D. Dingli, M. D. Cascino, K. Josic´, S. J. Russell, Zˇ . Bajzer, Mathematical modeling of cancer radiovirotherapy, Math. Biosci., 199 (2006), 55–78
-
[8]
D. Dingli, C. Offord, R. Myers, K.-W. Peng, T. W. Carr, K. Josic, S. J. Russell, Z. Bajzer, Dynamics of multiple myeloma tumor therapy with a recombinant measles virus, Cancer Gene Ther., 16 (2009), 873–882
-
[9]
R. Durrett, S. Levin, Spatial aspects of interspecific competition, Theor. Popul. Biol., 53 (1998), 30–43
-
[10]
M. El Younoussi, Z. Hajhouji, K. Hattaf, N. Yousfi, Dynamics of a reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response, Chaos Solitons Fractals, 157 (2022), 11 pages
-
[11]
G. I. Evan, K. H. Vousden, Proliferation, cell cycle, and apoptosis in cancer, Nature, 411 (2020), 342–348
-
[12]
A. Friedman, J. P. Tian, G. Fulci, E. A. Chiocca, J. Wang, Glioma virotherapy: effects of innate immune suppression and increased viral replication capacity, Cancer Res., 66 (2006), 2314–2319
-
[13]
K. Fujii, Complexity-stability relationship of two-prey-one-predator species system model: local and global stability, J. Theoret. Biol., 69 (1977), 613–623
-
[14]
V. Hutson, G. T. Vickers, A criterion for permanent coexistence of species, with an application to a two-prey one-predator system, Math. Biosci., 63 (1983), 253—269
-
[15]
E. Kelly, S. J. Russel, History of Oncolytic Viruses: Genesis to Genetic Engineering, Mol. Ther., 15 (2007), 651–659
-
[16]
M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, New York (2015)
-
[17]
C. Offord, Z. Bajzer, A hybrid global optimization algorithm involving simplex and inductive search, Lect. Notes Comput. Sci., 2074 (2001), 680–688
-
[18]
H. T. Ong, M. M. Timm, P. R. Greipp, T. E. Witzig, A. Dispenzieri, S. J. Russell, K.-W. Peng, Oncolytic measles virus targets high CD46 expression on multiple myeloma cells, Exp. Hematol., 34 (2006), 713–720
-
[19]
L. R. Paiva, C. Binny, S. C. Ferreira, Jr., M. L. Martins, A multiscale mathematical model for oncolytic virotherapy, Cancer Res., 69 (2009), 1205–1211
-
[20]
T. A. Phan, J. P. Tian, The Role of the Innate Immune System in Oncolytic Virotherapy, Comput. Math. Methods Med., 6 (2017), 1–17
-
[21]
C. L. Reis, J. M. Pacheco, M. K. Ennis, D. Dingli, In silico evolutionary dynamics of tumor virotherapy, Integr. Biol., 2 (2010), 41–45
-
[22]
D. M. Rommelfanger, C. P. Offord, J. Dev, Z. Bajzer, R. G. Vile, D. Dingli, Dynamics of melanoma tumor therapy with vesicular stomatitis virus: explaining the variability in outcomes using mathematical modeling, Gene Ther., 19 (2012), 543–549
-
[23]
J. P. Tian, The Replicability of Oncolytic Virus: Defining Conditions in Tumor Virotherapy, Math. Biosci. Eng., 8 (2011), 841–860
-
[24]
Y. Takeuchi, N. Adachi, Existence and bifurcation of stable equilibrium in two-prey, one-predator communities, Bull. Math. Biol., 45 (1983), 877–900
-
[25]
P. Van Den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48
-
[26]
L. M. Wein, J. T. Wu, D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: Implications for virus design and delivery, Cancer Res., 63 (2003), 1317–1324
-
[27]
D. Wodarz, Viruses as antitumor weapons: defining conditions for tumor remission, Cancer Res., 61 (2001), 3501–3507
-
[28]
D. Wodarz, Gene Therapy for Killing p53-Negative Cancer Cells: Use of Replicating Versus Nonreplicating Agents, HUM. Gene Ther., 14 (2003), 153–159
-
[29]
D. Wodarz, Computational approaches to study oncolytic virutherapy: insights and challenges, Gene Ther. Mol. Biol., 8 (2004), 137–146
-
[30]
D. Wodarz, A. Hofacre, J. W. Lau, Z. Sun, H. Fan, N. L. Komarova, Complex spatial dynamics of oncolytic viruses in vitro: mathematical and experimental approaches, PLoS Comput. Biol., 8 (2012), 1–8
-
[31]
D. Wodarz, N. Komarova, Towards predictive computational models of oncolytic virus therapy: Basis for experimental validation and model selection, PLoS One, 4 (2009), 1–9
-
[32]
J. T. Wu, H. M. Byrne, D. H. Kirn, L. M. Wein, Modeling and analysis of a virus that replicates selectively in tumor cells, Bull. Math. Biol., 63 (2001), 731–768
-
[33]
J. T. Wu, D. H. Kirn, L. M. Wein, Analysis of a three-way race between tumor growth, a replication-competent virus, and an immune response, Bull. Math. Biol., 66 (2004), 605–625