This paper deals with a procedure for combined therapies against cancer using oncolytic viruses and inhibitors. Replicating genetically modified adenoviruses infect cancer cells, reproduce inside them and eventually cause their death (lysis). As infected cells die, the viruses inside them are released and then proceed to infect other tumor cells. The successful entry of virus into cancer cells is related to the presence of the coxsackie-adenovirus receptor (CAR). Mitogen-activated protein kinase kinase (known as MEK) inhibitors can promote CAR expression, resulting in enhanced adenovirus entry into cancer cells. However, MEK inhibitors can also cause G1 cell-cycle arrest, inhibiting reproduction of the virus. To design an effective synergistic therapy, the promotion of virus infection must be optimally balanced with inhibition of virus production. We introduce a mathematical model to describe the effects of MEK inhibitors and viruses on tumor cells, and use it to explore the reduction of the tumor size that can be achieved by the combined therapies. Furthermore, we find an optimal dose of inhibitor: Poptimal = 1 - μ/δ for a certain initial density of cells (where μ is the removal rate of the dead cells and δ is the death rate of the infected cells). The optimal timing of MEK inhibitors is also numerically studied.
