Time delay induces a back to back Hopf bifurcation on oncolytic virotherapy.

Abstract

This study analyzes a basic mathematical model for the dynamic interactions among tumor cells, infected tumor cells and viruses population, focusing on the viral lytic cycle for oncolytic virotherapy. I study the time delay effect of viral infection on tumor cell populations by identifying bifurcation thresholds in both the burst rate and time delay of viral infection in oncolytic virus therapy. Time delay plays an important role in changing the structure of tumor cell populations in a dynamical system. The multi-bifurcation thresholds of the time delay are observed and also dependent on the bursting rate. This study demonstrates a strong relationship between viral burst rates and time delays in population dynamics. The results of this study show that time delay affects oscillation generation and results in back-to-back Hopf bifurcation. This study provides insight into understanding the relationship between the two control parameters, in which tumor cell populations pattern from equilibrium steady-state solutions to periodic solutions and from periodic solutions to equilibrium-state solutions.