Research article

A mathematical model of oncolytic virotherapy with time delay

  • Received: 16 September 2018 Accepted: 28 January 2019 Published: 06 March 2019
  • Oncolytic virotherapy is an emerging treatment modality which uses replication-competent viruses to destroy cancers without causing harm to normal tissues. By the development of molecular biotechnology, many e ective viruses are adapted or engineered to make them cancer-specific, such as measles, adenovirus, herpes simplex virus and M1 virus. A successful design of virus needs a full understanding about how viral and host parameters influence the tumor load. In this paper, we propose a mathematical model on the oncolytic virotherapy incorporating viral lytic cycle and virus-specific CTL response. Thresholds for viral treatment and virus-specific CTL response are obtained. Di erent protocols are given depending on the thresholds. Our results also support that immune suppressive drug can enhance the oncolytic e ect of virus as reported in recent literature.

    Citation: Zizi Wang, Zhiming Guo, Hal Smith. A mathematical model of oncolytic virotherapy with time delay[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 1836-1860. doi: 10.3934/mbe.2019089

    Related Papers:

  • Oncolytic virotherapy is an emerging treatment modality which uses replication-competent viruses to destroy cancers without causing harm to normal tissues. By the development of molecular biotechnology, many e ective viruses are adapted or engineered to make them cancer-specific, such as measles, adenovirus, herpes simplex virus and M1 virus. A successful design of virus needs a full understanding about how viral and host parameters influence the tumor load. In this paper, we propose a mathematical model on the oncolytic virotherapy incorporating viral lytic cycle and virus-specific CTL response. Thresholds for viral treatment and virus-specific CTL response are obtained. Di erent protocols are given depending on the thresholds. Our results also support that immune suppressive drug can enhance the oncolytic e ect of virus as reported in recent literature.


    加载中


    [1] R. Dunia and T. F. Edgar, Modeling of tumor growth undergoing virotherapy, Comput. Biol. Med., 41 (2011), 922–935.
    [2] S. J. Ries and C. H. Brandts, Oncolytic viruses for the treatment of cancer: current strategies and clinical trials, Drug Discov. Today, 9 (2004), 759–768.
    [3] M. J. Vähä-Koskela, J. E. Heikkilä and A. E. Hinkkanen, Oncolytic viruses in cancer therapy, Cancer Lett., 254 (2007), 178–216.
    [4] L. M. Wein, J. T. Wu, and D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment, Cancer Res., 63 (2003), 1317–1324.
    [5] N. L. Komarova and D. Wodarz, ODE models for oncolytic virus dynamics, J. Theor. Biol., 263 (2010), 530–543.
    [6] K. Garber, China approves world's first oncolytic virus therapy for cancer treatment, J. Natl. Cancer Inst., 98 (2006), 298–300.
    [7] J. M. Markert, M. D. Medlock, S. D. Rabkin, et al., Conditionally replicating herpes simplex virus mutant, G207 for the treatment of malignant glioma: results of a phase I trial, Gene Ther., 7 (2000), 867–874.
    [8] L. K. Csatary, G. Gosztonyi, J. Szeberenyi, et al., MTH-68/H Oncolytic Viral Treatment in Human High-Grade Gliomas, J. Neuro-Oncol., 67 (2004), 83–93.
    [9] Y. Lin, H. Zhang, J. Liang, et al., Identification and characterization of alphavirus M1 as a selective oncolytic virus targeting ZAP-defective human cancers, Proc. Natl. Acad. Sci. USA, 111 (2014), 4504–4512.
    [10] D. Wodarz, Viruses as antitumor weapons, Cancer Res., 61 (2001), 3501–3507.
    [11] J. Heaney, T. Barrett, and S. L. Cosby, Inhibition of in vitro leukocyte proliferation by morbilliviruses, J. Virol., 76 (2002), 3579–3584.
    [12] Ž. Bajzer, T. Carr, K. Josi´c, et al., Modeling of cancer virotherapy with recombinant measles viruses, J. Theor. Biol., 252 (2008), 109–122.
    [13] D. Dingli, M. D. Cascino, K. Josi´c, et al., Mathematical modeling of cancer radiovirotherapy, Math. Biosci., 199 (2006), 55–78.
    [14] Y. Wang, J. P. Tian and J. Wei, Lytic cycle: A defining process in oncolytic virotherapy, Appl. Math. Model., 37 (2013), 5962–5978.
    [15] E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 1144–1165.
    [16] B. R. Dix, S. J. O'Carroll, J. Colleen, et al., Efficient induction of cell death by adenoviruses requires binding of E1B55k and p53, Cancer Res., 60 (2000), 2666–2672.
    [17] A. R. Hall, B. R. Dix, S. J. O'Carroll, et al., p53-dependent cell death/apoptosis is required for a productive adenovirus infection, Nat. Med., 4 (1998), 1068–1072.
    [18] J. N. Harada and A. J. Berk, p53-Independent and -Dependent Requirements for E1B-55K in Adenovirus Type 5 Replication, J. Virol., 4 (1999), 5333–5344.
    [19] M. Ramachandra, A. Rahman, A. Zou, et al., Re-engineering adenovirus regulatory pathways to enhance oncolytic specificity and efficacy, Nat. Biotechnol., 19 (2001), 1035–1041.
    [20] G. Gonzalez-Parra, H. M. Dobrovolny, D. F. Aranda, et al., Quantifying rotavirus kinetics in the REH tumor cell line using in vitro data, Virus Res., 244 (2018), 53–63.
    [21] J. A. Borghans, R. J. de Boer and L. A. Segel, Extending the quasi-steady state approximation by changing variables, Bull. Math. Biol., 58 (1996), 43–63.
    [22] A. Friedman, J. P. Tian, G. Fulci, et al., Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity, Cancer Res., 66 (2006), 2314–2319.
    [23] K. Li, J. Liang, Y. Lin, et al., A classical PKA inhibitor increases the oncolytic effect of M1 virus via activation of exchange protein directly activated by cAMP 1, Oncotarget, 7 (2016), 48443– 48455.
    [24] V. L. de Rioja, N. Isern and J. Fort, A mathematical approach to virus therapy of glioblastomas, Biol. Direct, 11 (2016), 1.
    [25] J. T. Wu, D. H. Kirn and 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.
    [26] H. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653.
    [27] H. L. Smith, An introduction to delay differential equations with applications to the life sciences, Texts in Applied Mathematics.
    [28] H. L. Smith and H. R. Thieme, Dynamical systems and population persistence, American Mathematical Soc., 118 (2011).
    [29] J. T.Wu, H. M. Byrne, D. H. Kirn, et al., Modeling and analysis of a virus that replicates selectively in tumor cells, Bull. Math. Biol., 63 (2001), 731–768.
    [30] Z. Wang, Z. Guo and H. Peng, A mathematical model verifying potent oncolytic efficacy of M1 virus, Math. Biosci., 63 (2001), 731–768.
    [31] Z. Wang, Z. Guo and H. Peng, Dynamical behavior of a new oncolytic virotherapy model based on gene variation, Discrete Cont. Dyn. S., 10 (2017), 1079–1093.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4472) PDF downloads(1149) Cited by(7)

Article outline

Figures and Tables

Figures(13)  /  Tables(5)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog