Stability and Bifurcation Analysis for a Hepatitis C Virus Transmissions Model with Time Delay

In this paper, we propose a Hepatitis C virus transmissions model with time delay. Firstly, we get the condition for the existence and local stability of equilibria of the system. Secondly, by choosing the time delay τ as a bifurcation parameter, we show that Hopf bifurcation will occur as the time delay τ passes through some critical values. Thirdly, by use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, some numerical simulations is provided to verify the theoretical results.