Wavelet Collocation Method for HIV-1/HTLV-I Co-Infection Model Using Hermite Polynomial

Area of Science:

• Mathematical Biology
• Virology
• Numerical Analysis

Background:

• Co-infection with Human Immunodeficiency Virus type 1 (HIV-1) and Human T-lymphotropic Virus type I (HTLV-I) presents complex dynamics.
• Understanding the interplay between these viruses is crucial for effective treatment strategies.

Purpose of the Study:

• To analyze the dynamic behavior of a fractional order co-infection model involving HIV-1 and HTLV-I.
• To investigate the existence, uniqueness, positivity, boundedness, and stability of the model's solutions.
• To explore the impact of fractional orders on viral dynamics.

Main Methods:

• Application of the Hermite wavelet collocation method with operational matrices for numerical solutions.
• Utilizing fixed-point theory to establish the existence and uniqueness of solutions.
• Employing Lyapunov functions and LaSalle invariance principle for global stability analysis.
• Investigating Ulam-type stability and convergence properties of the numerical scheme.

Main Results:

• The Hermite wavelet method provides an accurate, stable, and efficient numerical solution for the nonlinear fractional co-infection model.
• Positivity and boundedness of solutions were demonstrated, ensuring biological relevance.
• Global stability of equilibrium points was established, offering insights into disease persistence or eradication.
• Variations in model dynamics were observed with different fractional order values.

Conclusions:

• The fractional order co-infection model, analyzed via Hermite wavelets, offers a robust framework for studying HIV-1/HTLV-I interactions.
• The numerical scheme is reliable and accurate, suitable for complex biological systems.
• Findings provide valuable mathematical insights for biologists and clinicians in managing HIV-1 and HTLV-I co-infections.