Chaos and bifurcations of a two-dimensional hepatitis C virus model with hepatocyte homeostasis.

This article focuses on the local dynamics, bifurcation analysis, and chaos control in a discrete two-dimensional mathematical model of hepatitis C virus (HCV) infection incorporating hepatocyte homeostasis. The study identifies equilibrium solutions—including liver-free, disease-free, total-infection, and partial-infection states—and analyzes their local stability using linear stability theory. It rigorously characterizes bifurcation sets, such as flip and Neimark–Sacker bifurcations, and applies bifurcation theory to determine conditions under which these bifurcations occur. To manage chaos arising from these bifurcations, the paper employs control strategies including the Ott–Grebogi–Yorke (OGY) method and hybrid control feedback, with numerical simulations validating the theoretical findings. The work concludes with suggestions for future research on codimension-two bifurcations and global dynamics of the discrete HCV model.