# On dynamics of fractional-order oncolytic virotherapy models

Volume 20, Issue 2, pp 79--87
Publication Date: October 19, 2019 Submission Date: May 04, 2019 Revision Date: August 09, 2019 Accteptance Date: August 17, 2019
• 3207 Views

### Authors

Abdullah Abu-Rqayiq - Department of Mathematics and Statistics, Texas A \& M University-Corpus Christi, Texas, 78412-5825, USA. Mohammad Zannon - Department of Mathematics and Statistics, Tafilah Technical University, Tafilah, Jordan.

### Abstract

In this paper, we provide a mathematical model with a fractional-order to investigate the dynamics of oncolytic virotherapy. We focus on how the dynamics of oncolytic virotherapy models can rely on the burst size of the virus. The burst size of a virus is the number of new viruses released from the lysis of an infected cell. Different viruses have different burst sizes. The numerical simulations confirm that the fractional-order differential models have the ability can provide accurate descriptions of oncolytic virotherapy models and capture the memory of the dynamics.

### Share and Cite

##### ISRP Style

Abdullah Abu-Rqayiq, Mohammad Zannon, On dynamics of fractional-order oncolytic virotherapy models, Journal of Mathematics and Computer Science, 20 (2020), no. 2, 79--87

##### AMA Style

Abu-Rqayiq Abdullah, Zannon Mohammad, On dynamics of fractional-order oncolytic virotherapy models. J Math Comput SCI-JM. (2020); 20(2):79--87

##### Chicago/Turabian Style

Abu-Rqayiq, Abdullah, Zannon, Mohammad. "On dynamics of fractional-order oncolytic virotherapy models." Journal of Mathematics and Computer Science, 20, no. 2 (2020): 79--87

### Keywords

• Fractional calculus
• oncolytic virotherapy
• immune innate response
• equilibrium points
• local stability

•  34D20

### References

• [1] E. Ahmad, A. M. A. El-Sayed, H. A. A. El-Saka, On some Routh-Hurwitz Conditions for fractional-order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems, Phys. Latt. A, 358 (2006), 1--4

• [2] Z. Bajzer, T. Carr, K. JosiÄ‡, S. J. Russell, D. Dingli, Modeling of cancer virotherapy with recombinant measles viruses, J. Theoret. Biol., 252 (2008), 109--122

• [3] N. Bellomo, A. Bellouquid, J. Nieto, J. Soler, Multiscale biological tissue models and flux limited chemotaxis from binary mixtures of multicellular growing systems, Math. Models Methods Appl. Sci., 20 (2010), 1179--1207

• [4] E. A. Chiocca, Oncolytic viruses, Nature Reviews Cancer, 2 (2002), 938--950

• [5] K. Diethelm, N. J. Ford, Analysis of freactional differential equations, J. Math. Anal. Appl., 265 (2002), 229--248

• [6] K. Diethelm, N. J. Ford, A. D. Freed, Detailed error analysis for a fractional Adams method, Numer. Algorithms, 36 (2004), 31--52

• [7] K. Diethelm, A. D. Freed, The Frac PECE subroutine for the numerical solution of differential equations of fractional order, in: Forschung und Wissenschaftliches Rechnen, 1999 (1999), 57--71

• [8] A. Friedman, J. P. Tian, E. A. Chiocca, J. Wang, Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity, Cancer Research, 66 (2006), 2314--2319

• [9] N. L. Komarova, D. Wodarz, ODE models for oncolyticvirus dynamics, J. Theoret. Biol., 263 (2010), 530--543

• [10] D. Matignon, Stability result on fractional differential equations with applications to control processing, Comput. Eng. Syst. Appl., 2 (1996), 963--968

• [11] A. S. Novozhilov, F. S. Berezovskaya, E. V. Koonin, G. P. Karev, Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models, Biology Direct, 1 (2006), 1--18

• [12] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)

• [13] J. A. Tenreiro Machado, Entropy analysis of integer and fractional dynamical systems, Nonlinear Dynam., 62 (2010), 371--378

• [14] J. P. Tian, The replicability of oncolytic virus: defining conditions in tumor virotherapy, Math. Biosci. Eng., 8 (2011), 841--860

• [15] 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 Research, 63 (2003), 1317--1324

• [16] D. Wodarz, Viruses as antitumor weapons: defining conditions for tumor remission, Cancer Research, 61 (2001), 3501--3507

• [17] D. Wodarz, Computational approaches to study oncolytic virutherapy: insights and challenges, Gene. Ther. Mol. Biol., 8 (2004), 137--146

• [18] 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