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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

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 effective 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. Different protocols are given depending on the thresholds. Our results also support that immune suppressive drug can enhance the oncolytic effect of virus as reported in recent literature.
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Keywords 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. Mathematical Biosciences and Engineering, 2019, 16(4): 1836-1860. doi: 10.3934/mbe.2019089


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