Stability Regions and Bifurcation Analysis of a Delayed Tumor Therapy Model Using Oncolytic Virus

We consider the dynamics of a tumor therapy model using oncolytic viruses with time delay. The model is a two-dimensional system of ordinary differential equations with a delay term that represents the latent period required for viral replication following the infection of tumor cells. Our study starts with the derivation of the positive equilibrium point and analyzes its local stability in both the absence and presence of delay terms. Subsequently, by using Pontryagin’s criterion, we establish the necessary and sufficient conditions for the asymptotic stability of the equilibrium point under the delay term. The numerical bifurcation analysis identifies a transcritical bifurcation in the nondelayed case, whereas the analytical analysis reveals a Hopf bifurcation in the delayed case, leading to sustained oscillations in the tumor cell population. These results suggest that the success of the virotherapy is sensitive to the delay effects. It implies that we need to consider time-dependent dynamics to determine effective treatment strategies.