Over the past few years, several studies have been made on cancer viral therapy. One of the major advantages of oncolytic virotherapy over standard cytotoxic chemotherapeutic agents is that tumor cell selectivity can potentially target and eliminate cancer cells without affecting normal cells. Therefore studies of the virus dynamics are needed for the purpose of cancer treatment, not the virus as the cause of the disease.
We introduce a deterministic and stochastic model of tumor-viral dynamics. For finding conditions of virotherapy failure, the local asymptotic stability and the global asymptotic stability of a virotherapy failure equilibrium are studied. By using the basic reproductive ratio, we investigate its sensitivity to the parameter values characterizing viruses. We also derive a system of stochastic differential equations that based on the deterministic model and explore the probability of uninfected tumor and infected tumor extinction. The analysis suggests that an oncolytic virus is desired with a high infection rate and optimal cytotoxicity for effective treatment. Recent investigators showed that the combination of viral therapy with chemotherapy may lead to synergistic mechanisms for eliminating cancer not achievable by either therapy alone. So our main problems are “Which combination therapy should we take for more effective treatment?” and “How can we measure and predict the quantity of synergy effect?”. Koizumi and Iwami suggested the estimation methods of the optimal dose point that is calculated from the difference between the effects of the combined drugs obtained by modeling the dynamics and the additive effects by Loewe additivity. Based on their ideas, we investigate a synergistic effect between oncolytic virus therapy and chemotherapy. Extended synergy concepts for combination therapy are discussed.