A study on fractional HBV model through singular and non-singular derivatives

Area of Science:

• Mathematical Biology
• Epidemiology
• Fractional Calculus

Background:

• Hepatitis B virus (HBV) infection remains a significant global health concern.
• Modeling disease dynamics is crucial for understanding transmission and control strategies.
• Fractional calculus offers advanced tools for capturing complex biological processes.

Purpose of the Study:

• To analyze the dynamics of an HBV model incorporating asymptomatic carriers.
• To compare the efficacy of Caputo and Atangana-Baleanu (ABC) fractional derivatives in modeling HBV.
• To introduce and evaluate novel numerical algorithms for fractional differential equations.

Main Methods:

• Mathematical analysis using fixed-point theory for existence and uniqueness of solutions.
• Implementation of generalized Adams-Bashforth-Moulton (ABM) method for Caputo derivatives.
• Application of an Adams-type predictor-corrector (PC) algorithm for ABC derivatives.
• Numerical simulations across a range of fractional-order values.

Main Results:

• Demonstrated the application of two distinct fractional derivatives (Caputo and ABC) in HBV modeling.
• Presented graphical comparisons of numerical results obtained using different fractional operators.
• Showcased the performance of advanced numerical algorithms (ABM and PC) for fractional models.
• Proposed a new variable-order fractional network model for enhanced disease spread insights.

Conclusions:

• The study successfully evaluated HBV model dynamics using distinct fractional calculus approaches.
• Numerical methods provide effective tools for analyzing fractional epidemic models.
• The proposed variable-order fractional network model holds promise for more realistic disease transmission modeling in connected populations.