Abstract: This work studies a triply haptotactic cross-diffusion system modeling oncolytic virotherapy. In 2019, Alzahrani et al. proposed a model to better understand the process of oncolytic virotherapy. However, mathematical studies on this model indicate that the uninfected cancer cells will exist globally in time, whereas the normal cells will die off. These results are far from the facts of clinical trials, which show that oncolytic virotherapy can control and decrease the overall cancer expansion. Hence the purpose of the present paper is to modify the previous model. Our new model reveals that oncolytic virotherapy can prevent outbreak of tumors whereas the tumors may outbreak without interference of the oncolytic viruses. More precisely and mathematically, there is a unique classical solution for this system with an associated no-flux initial-boundary condition, which is globally bounded. The result is consistent with clinical facts.
