Mathematical Biosciences and Engineering, 2011, 8(3): 841-860. doi: 10.3934/mbe.2011.8.841.

Primary: 34C23, 34C10; Secondary: 92B99.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

The replicability of oncolytic virus: Defining conditions in tumor virotherapy

1. Mathematics Department, College of William and Mary, Williamsburg, VA 23187

The replicability of an oncolytic virus is measured by its burst size. The burst size is the number of new viruses coming out from a lysis of an infected tumor cell. Some clinical evidences show that the burst size of an oncolytic virus is a defining parameter for the success of virotherapy. This article analyzes a basic mathematical model that includes burst size for oncolytic virotherapy. The analysis of the model shows that there are two threshold values of the burst size: below the first threshold, the tumor always grows to its maximum (carrying capacity) size; while passing this threshold, there is a locally stable positive equilibrium solution appearing through transcritical bifurcation; while at or above the second threshold, there exits one or three families of periodic solutions arising from Hopf bifurcations. The study suggests that the tumor load can drop to a undetectable level either during the oscillation or when the burst size is large enough.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Hopf bifurcation.; Virotherapy; burst size

Citation: Jianjun Paul Tian. The replicability of oncolytic virus: Defining conditions in tumor virotherapy. Mathematical Biosciences and Engineering, 2011, 8(3): 841-860. doi: 10.3934/mbe.2011.8.841

 

This article has been cited by

  • 1. Joseph Malinzi, Amina Eladdadi, Precious Sibanda, Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment, Journal of Biological Dynamics, 2017, 11, 1, 244, 10.1080/17513758.2017.1328079
  • 2. Yujie Wang, Jianjun Paul Tian, Junjie Wei, Lytic cycle: A defining process in oncolytic virotherapy, Applied Mathematical Modelling, 2013, 37, 8, 5962, 10.1016/j.apm.2012.12.004
  • 3. Yongmei Su, Chen Jia, Ying Chen, Optimal Control Model of Tumor Treatment with Oncolytic Virus and MEK Inhibitor, BioMed Research International, 2016, 2016, 1, 10.1155/2016/5621313
  • 4. Tuan Anh Phan, Jianjun Paul Tian, The Role of the Innate Immune System in Oncolytic Virotherapy, Computational and Mathematical Methods in Medicine, 2017, 2017, 1, 10.1155/2017/6587258
  • 5. Kent Bailey, Amber Kirk, Shruthi Naik, Rebecca Nace, Michael B. Steele, Lukkana Suksanpaisan, Xing Li, Mark J. Federspiel, Kah-Whye Peng, David Kirk, Stephen J. Russell, Brian Lichty, Mathematical Model for Radial Expansion and Conflation of Intratumoral Infectious Centers Predicts Curative Oncolytic Virotherapy Parameters, PLoS ONE, 2013, 8, 9, e73759, 10.1371/journal.pone.0073759
  • 6. Asim Timalsina, Jianjun Paul Tian, Jin Wang, Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity, Bulletin of Mathematical Biology, 2017, 79, 8, 1736, 10.1007/s11538-017-0304-3
  • 7. Daniel Santiago, Johannes Heidbuechel, Wendy Kandell, Rachel Walker, Julie Djeu, Christine Engeland, Daniel Abate-Daga, Heiko Enderling, Fighting Cancer with Mathematics and Viruses, Viruses, 2017, 9, 9, 239, 10.3390/v9090239
  • 8. 玉红 李, Dynamic Analysis of the Model of Brain Cancer Treatment by Pulse Infusion of Zika, Advances in Applied Mathematics, 2019, 08, 03, 439, 10.12677/AAM.2019.83050
  • 9. Joseph Malinzi, Mathematical Analysis of a Mathematical Model of Chemovirotherapy: Effect of Drug Infusion Method, Computational and Mathematical Methods in Medicine, 2019, 2019, 1, 10.1155/2019/7576591
  • 10. Jiantao Zhao, Jianjun Paul Tian, Spatial Model for Oncolytic Virotherapy with Lytic Cycle Delay, Bulletin of Mathematical Biology, 2019, 10.1007/s11538-019-00611-2

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved