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 which yield treatment failure or success. We show that the tumor size under therapy at a certain time is less than the tumor size without therapy. We determine the minimum tumor size by the therapy and parameter regions under which this minimum is attained. 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 alters 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 timescale of virus dynamics. Our results suggests that when timescale of virus dynamics is fast, administration of a more virulent virus leads into more tumor reduction. When 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 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.