A Dynamical Analysis on a Tumour Virotherapy Model with Standard Incident Rate

Abstract

This paper discusses a dynamical analysis on a model that governs the growth of tumour cell under a therapy by using oncolytic viruses, on the standard incident rate. The model is a modification of the similar one by replacing the bilinear incident rate with the standard one. The conducted dynamical analysis consists of the determination of equilibrium points and their existence conditions, followed by local as well as global stability analysis of the equilibrium points. The analytical result shows that there are two equilibrium points, namely uninfected and the endemic point, which needs a condition to exist. Stability analysis shows that there is a dimensionless basic reproduction number that marks the existence as well as the stability of equilibrium points. When basic reproduction number is less than one, there is only the uninfected equilibrium, which is global asymptotically stable. On the other hands, both of equilibrium points exist when the basic reproduction number is more than one, but the uninfected point is not stable anymore, while the endemic one is local asymptotically stable under a condition. Some numerical simulations are performed to illustrate the analytical result. Numerically, it can also be demonstrated that there is a set of parameters which indicates that tumour can be fully removed.

Keywords

• Tumour, Oncolytic Virotherapy, Standard Incident Rate, Stability Analysis