Hepatitis C virus fractional-order model: mathematical analysis.

Area of Science:

• Epidemiology
• Mathematical Biology
• Fractional Calculus

Background:

• Mathematical modeling is vital for predicting disease spread and informing public health policy.
• Hepatitis C Virus (HCV) infection dynamics require sophisticated models to understand transmission and control.

Purpose of the Study:

• To investigate a fractional-order differential mathematical model of HCV infection.
• To incorporate virus-to-cell and cell-to-cell transmission modes, alongside a cure rate.
• To analyze the long memory effects in disease dynamics using Caputo fractional derivatives.

Main Methods:

• Developed a four-compartment mathematical model (susceptible hepatocytes, infected, viral load, immune response).
• Employed fractional calculus, including Caputo derivatives, to model memory effects.
• Proved existence, positivity, and boundedness of solutions, analyzed steady states, and established global stability.
• Utilized numerical methods based on fractional calculus and Lagrange interpolation for validation.

Main Results:

• The free-endemic equilibrium is stable when the basic reproduction number is less than unity.
• Endemic equilibria demonstrate stability under specific optimal conditions.
• Numerical simulations align with theoretical results, validating the model's predictions.

Conclusions:

• The fractional-order model provides a robust framework for understanding HCV infection dynamics.
• The study highlights the importance of fractional calculus in capturing long-term memory effects in biological systems.
• Findings support evidence-based public health strategies for HCV control.