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

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Abstract
In this paper, we delve into the intricate local dynamics at equilibria within a two-dimensional model of hepatitis C virus (HCV) alongside hepatocyte homeostasis. The study investigates the existence of bifurcation sets and conducts a comprehensive bifurcation analysis to elucidate the system’s behavior under varying conditions. A significant focus lies on understanding how changes in parameters can lead to bifurcations, which are pivotal points where the qualitative behavior of the system undergoes fundamental transformations. Moreover, the paper introduces and employs hybrid control feedback and Ott–Grebogi–Yorke strategies as tools to manage and mitigate chaos inherent within the HCV model. This chaos arises due to the presence of flip and Neimark–Sacker bifurcations, which can induce erratic behavior in the system. Through the implementation of these control strategies, the study aims to stabilize the system and restore it to a more manageable and predictable state. Furthermore, to validate the theoretical findings and the efficacy of the proposed control strategies, extensive numerical simulations are conducted. These simulations serve as a means of confirming the theoretical predictions and provide insight into the practical implications of the proposed control methodologies. By combining theoretical analysis with computational simulations, the paper offers a comprehensive understanding of the dynamics of the HCV model and provides valuable insights into potential strategies for controlling and managing chaos in such complex biological systems.

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