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Khushbu Agrawal¹, Sunil Kumar¹

¹Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, 831014, India.

Advanced Biology

|August 10, 2024

Summary

This study analyzes a fractional co-infection model of HIV-1 and HTLV-I using Hermite wavelets. The research confirms model stability and provides insights for treating these viral infections.

Keywords:

chaotic behavior convergence analysis existence and uniqueness fractional order co‐infection model global and ulam hyres stability analysis hermite wavelet operational matrix numerical scheme positivity and boundedness

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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.