Optimal control of a basic model of oncolytic virotherapy

Volume 24, Issue 2, pp 119--126 http://dx.doi.org/10.22436/jmcs.024.02.03

Publication Date: January 21, 2021 Submission Date: August 13, 2020 Revision Date: November 21, 2020 Accteptance Date: December 17, 2020

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)

• 1409 Downloads
• 2699 Views

Authors

Abdullah Abu-Rqayiq - Department of Mathematics \(\&\) Statistics, Texas A\(\&\)M University, Corpus Christi, Texas 78412, U.S.A.. Haneen Alayed - Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, U.S.A.. Mohammad Zannon - Department of Mathematics \(\&\) Statistics, Tafilah Technical University, At-Tafilah, Jordan.

Abstract

This paper applies an optimal control approach to study the dynamics of a basic Oncolytic Virotherapy model. This study applies mathematical modeling based on an established basic oncolytic virotherapy model for tumor growth. Choosing an appropriate control strategy is essential to reduce the cost of the therapy. By applying optimal control theory, we seek to minimize the cost of virotherapy and reduce the load of tumor cells. The existence of optimal control is proved. State solution given an optimal strategy and the optimal control is determined. Numerical simulation is carried out to visualize and support our results.

Share and Cite

Keywords

• Oncolytic virotherapy
• optimal control
• tumor cells
• hamiltonian

MSC

•  92C50
•  93A30
•  37N35
•  34K28

References

• [1] A. Abu-Rqayiq, M. Zannon, On Dynamics of Fractional Order Oncolytic Virotherapy Models, J. Math. Computer Sci., 20 (2020), 79--87
  • View Article
  • Google Scholar


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


• [3] W. H. Fleming, R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York (1975)
  • View Article
  • Google Scholar


• [4] A. Friedman, J. P. Tian, G. Fulci, E. A. Chiocca, J. Wang, Glioma Virotherapy: Effect of Innate Immune Suppression and Increased Viral Replication Capacity, Cancer Res., 66 (2006), 2314--2319
  • View Article
  • Google Scholar


• [5] N. L. Komarova, D. Wodarz, ODE models for oncolytic virus dynamics, J. Theoret. Biol., 263 (2010), 530--543
  • View Article
  • Google Scholar


• [6] R. M. Neilan, S. Lenhart, An Introduction to Optimal Control with an Application in Disease Modeling, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 75 (2010), 67--81
  • View Article
  • Google Scholar


• [7] 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, Biol. Direct, 6 (2006), 1--18
  • View Article
  • Google Scholar


• [8] J. P. Tian, The Replicability of Oncolytic Virus: Defining Conditions in Tumor Virotherapy, Math. Biosci. Eng., 8 (2011), 841--860
  • View Article
  • Google Scholar


• [9] 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
  • View Article
  • Google Scholar


• [10] D. Wodarz, Viruses as antitumor weapons: defining conditions for tumor remission, Cancer Res., 61 (2001), 3501--3507
  • View Article
  • Google Scholar


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


• [12] 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
  • View Article
  • Google Scholar