Optimal control of virotherapy in a tumor model

Oncolytic virotherapy results in the use of genetically-modified viruses in order to infect tumor cells while safeguarding healthy cells. Here we propose two novel mathematical models, based on known formulations used in SIR-type models and applied to cancer modeling, that describe the interaction between three populations, i.e. tumor cells, infected tumor cells and virus particles, for small and large tumors, by assuming density and frequency-dependent virus transmission, respectively. Both the infection due to the virus and to the infected tumor cells were considered, as well as the mortality of the cells due to the activation of the immune system by the virus population itself, features encountered in the vaccinia virus population. Moreover, we assumed that the tumor cells grow following a generalized logistic law. For both models, an optimal control problem is formulated to find the time-dependent virus input needed to minimize tumour burden while accounting for treatment costs and toxicity. Our results also show that, for certain parameter regimes, oscillatory virus–tumour dynamics can emerge, which may transiently suppress tumour load and are relevant for designing effective therapeutic strategies. One of the main results indicates that successful viral propagation through the tumour requires that infected cells are not removed too rapidly, primarily through virus-induced lysis, compared to uninfected cells. If the effective clearance of infected cells is too high, the virus cannot spread efficiently and treatment becomes unsuccessful.