Dynamics of a mathematical model of oncolytic virotherapy with tumor-Virus interaction

Volume 31, Issue 4, pp 461--476 http://dx.doi.org/10.22436/jmcs.031.04.08

Publication Date: May 30, 2023 Submission Date: March 15, 2023 Revision Date: March 31, 2023 Accteptance Date: May 10, 2023

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Authors

A. Abu-Rqayiq - Concord University , Athens, WV, 24712, USA. H. Alayed - New Mexico State University, Las Cruces, NM, 88001, USA.

Abstract

Virotherapy is a cancer treatment that uses a virus that can target cancer cells to infect, replicate, and destroy them leaving the healthy cells unharmed. Recently, considerable efforts have been made to understand the mechanisms and dynamics of oncolytic virotherapy. In this paper, we study the dynamics of a basic model of oncolytic tumor virotherapy. This model emphasizes the interaction between cancer-infected cells and cancer uninfected cells. To understand some of the consequences of this contact from a mathematical point of view, we study the dynamics behavior of the model and present a qualitative analysis of the equilibria. To illustrate which parameters in the model affect the outcome of virotherapy the most, we determine bifurcation parameters and conduct a sensitivity analysis of the model's parameters. Numerical simulations are conducted to show the validity of our analysis.

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Keywords

• Cancer
• oncolytic virotherapy
• stability
• Lyapunov
• basic reproductive number

MSC

•  92C50
•  93A30
•  37N35
•  34K28

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