Chaos and Bifurcations of a Discrete HCV Model with Density-Dependent Proliferation

In this paper, we explore the dynamical behavior of a discrete Hepatitis C Virus (HCV) model with density-dependent proliferation. More precisely, we first explore the local dynamics at steady states and then give detailed bifurcation analysis to the discrete HCV model. It is proved that discrete HCV model does not undergo period-doubling bifurcation at liver-free, disease-free and total infection steady states but it undergoes period-doubling and Neimark–Sacker bifurcations at partial infection steady-state. Further, chaos control is also examined by OGY and hybrid control feedback strategies. Finally, the obtained theoretical results are confirmed numerically.