Hopf bifurcation analysis in a delayed oncolytic virus dynamics with continuous control

A delayed oncolytic virus dynamics with continuous control is investigated. The local stability of the infected equilibrium is discussed by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to support the theoretical results.