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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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Kyungpook Mathematical Journal 2022; 62(1): 119-132

Published online March 31, 2022 https://doi.org/10.5666/KMJ.2022.62.1.119

Copyright © Kyungpook Mathematical Journal.

Hopf-bifurcation Analysis of a Delayed Model for the Treatment of Cancer using Virotherapy

Maharajan Rajalakshmi and Mini Ghosh*

Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, Chennai-600127, India
e-mail : rajalakshmi.m2016@vitstudent.ac.in and minighosh@vit.ac.in

Received: February 23, 2020; Revised: October 7, 2020; Accepted: November 16, 2020

Abstract

Virotherapy is an effective method for the treatment of cancer. The oncolytic virus specifically infects the lyse cancer cell without harming normal cells. There is a time delay between the time of interaction of the virus with the tumor cells and the time when the tumor cells become infectious and produce new virus particles. Several types of viruses are used in virotherapy and the delay varies with the type of virus. This delay can play an important role in the success of virotherapy. Our present study is to explore the impact of this delay in cancer virotherapy through a mathematical model based on delay differential equations. The partial success of virotherapy is guarenteed when one gets a stable non-trivial equilibrium with a low level of tumor cells. There exits Hopf-bifurcation by considering the delay as bifurcation parameter. We have estimated the length of delay which preserves the stability of the non-trivial equilibrium point. So when the delay is less than a threshold value, we can predict partial success of virotherapy for suitable sets of parameters. Here numerical simulations are also performed to support the analytical findings.

Keywords: Cancer, Virotherapy, Delay model, Hopf-bifurcation