Global dynamics of an age-dependent multiscale hepatitis C virus model

Area of Science:

• Virology
• Mathematical Biology
• Epidemiology

Background:

• Hepatitis C virus (HCV) infection dynamics involve complex interactions within host cells and at the RNA level.
• Understanding the long-term behavior of HCV is crucial for developing effective treatment strategies.

Purpose of the Study:

• To investigate the global dynamics of a multiscale mathematical model for Hepatitis C virus (HCV) infection.
• To establish conditions for the theoretical extinction or persistence of HCV within host cells.

Main Methods:

• Development of a multiscale mathematical model incorporating viral evolution in cells and RNA.
• Analysis of model equilibria (infection-free and infected) using eigenvalue analysis and Lyapunov functions.
• Application of persistence theory to determine the long-term fate of the virus.

Main Results:

• The basic reproduction number (R0) for the HCV model was determined.
• The existence of an infected equilibrium was established when R0 > 1.
• Global asymptotic stability of both infection-free (R0 < 1) and infected (R0 > 1) equilibria was proven.

Conclusions:

• The study provides a theoretical framework to predict HCV extinction or persistence based on the basic reproduction number.
• Mathematical analysis confirms the stability of both disease-free and endemic states in the HCV model.
• Numerical simulations support the theoretical findings on viral dynamics.