Two‐Dimensional Hepatitis C Virus Model With Chaos, Stability, and Bifurcations

ABSTRACT In this paper, we explore the local stability, chaos, and bifurcations of a discrete hepatitis C virus model. More precisely, it is proved that for all model's parameters, model has liver‐free and disease‐free solutions, but it has total‐infection and partial‐infection solutions under certain parametric conditions. Further, we first constructed the linearized system and then local behavior at equilibria of a discrete hepatitis C virus model is explored by the linear stability theory. Next, for deeper understanding the complex dynamics of the discrete hepatitis C virus model, we first identified the bifurcation sets and then detail bifurcation analysis at equilibria is explored by the bifurcation theory. Furthermore, chaos in the hepatitis C virus model is studied due to the appearance of Neimark–Sacker and flip bifurcations by OGY and hybrid control feedback strategies, respectively. Finally, theoretical results are confirmed numerically.