In this study, we present and analyze a new mathematical model for the dynamics of hepatitis C virus (HCV) infection. The model incorporates key biological factors, including the logistic growth of healthy hepatocytes, intracellular delays, diffusion, viral entry into host cells, and virus transmission between cells. We first establish the existence and boundedness of the model’s solution. Our results show that if the basic reproduction number \(\mathcal {R}_0\) is below 1, the virus cannot persist, while if \(\mathcal {R}_0\) exceeds 1, the virus persists uniformly. By analyzing the characteristic equation and applying normal form theory and the center manifold theorem to partial functional differential equations, we confirm a Hopf bifurcation at the positive equilibrium point, deriving properties of the resulting periodic solutions. Furthermore, a controller is incorporated into the model, and adjusting control parameters can broaden the stability domain, shift the Hopf bifurcation point, and modify the associated periodic solutions. Numerical simulations show that introducing delay and control mechanisms can lead to complex dynamics. This study is novel in its incorporation of both intracellular delays and control strategies, offering new insights into the dynamic behavior of HCV infection compared to previous models.
