A mathematical model of oncolytic virotherapy with time delay

Zizi Wang; Zhiming Guo; Hal Smith; Zizi Wang; Zhiming Guo; Hal Smith

doi:10.3934/mbe.2019089

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 1836-1860. doi: 10.3934/mbe.2019089

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Research article

A mathematical model of oncolytic virotherapy with time delay

1.
School of Mathematics and Electronic Engineering, Wenzhou University, Wenzhou, 325035, PR China
2.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, PR China
3.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

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.
- oncolytic virotherapy,
- immune response,
- delay differential equation,
- stability,
- hopf bifurcation
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

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Abstract

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.

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