A mathematical approach to effects of CTLs on cancer virotherapy in the second injection of virus

This paper proposes a planar delay differential equation for cancer virotherapy. The model simulates the situation in which an oncolytic virus is injected for the second time, and the immune system suppresses the viral infection with a time delay. Our purpose is to provide theoretical conditions so that the therapy can be continued successfully. With the help of the characteristic equation, we examine the singularities and their local stability. Hopf bifurcation is also investigated around the endemic singularity. It is shown that there is a sequence of Hopf bifurcations, but the Hopf cycles do not persist continuously between the two sequential bifurcations. Finally, we see that virotherapy can be conducted successfully by controlling the delay parameter.