Fighting cancer with oncolytic viral therapy: identifying threshold parameters for success

We model interactions between cancer cells and free virus during oncolytic viral therapy. One of our main goals is to identify parameter regions that yield treatment failure or success. We show that the tumor size under therapy at a particular time is less than the size without therapy. Our analysis shows there are two thresholds for the horizontal transmission rate: a "Control threshold", the threshold above which treatment is efficient, and an "optimum threshold", the threshold beyond which infection prevalence reaches 100% and the tumor shrinks to its smallest size. Moreover, we explain how changes in the virulence level of the free virus alter the optimum threshold and the minimum tumor size. We identify a threshold for the virulence level of the virus and show how this threshold depends on the timescale of virus dynamics. Our results suggest that when the timescale of virus dynamics is fast, the administration of a more virulent virus leads to more tumor reduction. Conversely, when the viral timescale is slow, a higher virulence will have drawbacks on the results, such as high amplitude oscillations. Furthermore, our numerical observation depicts fast and slow dynamics. Our numerical simulations indicate there exists a two-dimensional globally attracting surface that includes the unstable manifold of the interior equilibrium. All solutions with positive initial conditions rapidly approach this two-dimensional attracting surface. In contrast, the trajectories on the attracting surface slowly tend to the periodic solution. HighlightsO_LIThe assumption that the viral load is in a quasi-steady state is relaxed, and infected cells are assumed to be mitotic. C_LIO_LIOur model strongly suggests that the tumor size is always reduced by therapy. C_LIO_LIWe identify minimum tumor size, control threshold, and optimum threshold of the therapy. C_LIO_LIOur analysis shows optimal virulence level of oncolytic virus depends on the time scale of virus dynamics. C_LIO_LIWhen virus dynamic is slow, highly virulent virus causes long remission before relapse. C_LI