A novel hybrid method with convergence analysis for approximation of HTLV-I dynamics model

Area of Science:

• Mathematical Biology
• Numerical Analysis
• Virology

Background:

• Human T-cell lymphotropic virus I (HTLV-I) infection models are crucial for understanding viral pathogenesis.
• Fractional calculus offers a more comprehensive framework for modeling complex biological processes like viral infections.
• Existing numerical methods may face challenges in accurately and efficiently solving these fractional models.

Purpose of the Study:

• To develop and validate a novel numerical method for approximating solutions to HTLV-I infection models.
• To enhance the accuracy and efficiency of solving fractional differential equations relevant to virology.
• To provide a reliable computational tool for researchers studying HTLV-I.

Main Methods:

• Utilizing the operational matrix and spectral method to transform fractional differential equations into algebraic systems.
• Employing the Levenberg-Marquardt algorithm for efficient solution of the resulting nonlinear equations.
• Conducting theoretical convergence analysis and error bound estimations to ensure method validity.

Main Results:

• The proposed numerical method effectively converts fractional HTLV-I models into solvable nonlinear algebraic systems.
• The Levenberg-Marquardt algorithm demonstrates high efficiency in solving these systems.
• Theoretical analysis confirms the convergence and accuracy of the approach, with error bounds established.
• Numerical simulations on test problems show superior performance compared to existing methods.

Conclusions:

• The novel numerical approach, combining spectral methods and the Levenberg-Marquardt algorithm, is a reliable and efficient technique for solving HTLV-I fractional models.
• This method offers a significant advancement in the computational study of viral infections.
• The findings pave the way for more accurate predictions and analyses in HTLV-I research.