<abstract><p>A mathematical model of tumor-immune system interactions with an oncolytic virus therapy for which the immune system plays a twofold role against cancer cells is derived. The immune cells can kill cancer cells but can also eliminate viruses from the therapy. In addition, immune cells can either be stimulated to proliferate or be impaired to reduce their growth by tumor cells. It is shown that if the tumor killing rate by immune cells is above a critical value, the tumor can be eradicated for all sizes, where the critical killing rate depends on whether the immune system is immunosuppressive or proliferative. For a reduced tumor killing rate with an immunosuppressive immune system, that bistability exists in a large parameter space follows from our numerical bifurcation study. Depending on the tumor size, the tumor can either be eradicated or be reduced to a size less than its carrying capacity. However, reducing the viral killing rate by immune cells always increases the effectiveness of the viral therapy. This reduction may be achieved by manipulating certain genes of viruses via genetic engineering or by chemical modification of viral coat proteins to avoid detection by the immune cells.</p></abstract>

We investigate therapeutic effects of monotherapy of oncolytic viruses, of adopted cell transfer, as well as the two combined therapies over a short time treatment period by applying optimal control techniques. The goal is to minimize the number of susceptible tumor cells and the costs associated with the therapy over the treatment period. We verify that there exists an optimal control pair and derive the necessary conditions. The optimality system is solved numerically to provide optimal protocols under different scenarios with respect to initial tumor sizes and parameter values. Although the two types of therapy do not work synergistically when the viral killing rate by immune cells is large, a small anti-viral killing can improve therapy success of either monotherapy of oncolytic viruses or combined therapy of oncolytic viruses and adopted T cell transfer. This finding can be accomplished either by manipulating certain genes of viruses via genetic engineering or by chemical modification of viral coat proteins to avoid detection by the immune cells.

We propose and study a mathematical model governing interactions between cancer and immune system with an oncolytic viral therapy (OVT), wherein cancer cells can activate and inhibit immune cells simultaneously with saturations.When the therapy is not applied, it is shown that the interaction can support at most three hyperbolic positive equilibria where two of them are always asymptotically stable and the other is a saddle point. The reachable stable tumor burden can be either small or large depending on initial tumor size. We analyze the full model by proving global asymptotic stability of the virus-free equilibrium that corresponds to OVT failure. Sufficient conditions based on model parameters are derived under which the model is uniformly persistent. The proposed system is validated using a mouse model of human pancreatic cancer carried out by Koujima et al. Global sensitivity analysis indicates that the rates of tumor-mediated killing and immune cell exhaustion are critical for tumor progression and therapy success. Numerical bifurcation analysis reveals that the saddle point can be utilized to estimate the maximum tumor load for eradication by OVT. Moreover, an immunosuppressive microenvironment may enhance viral therapy efficacy.