Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis...

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Bibliographic Details
Published in:Fractal and fractional 2024-05, Vol.8 (5), p.299
Main Authors: Anjam, Yasir Nadeem, Turki Alqahtani, Rubayyi, Alharthi, Nadiyah Hussain, Tabassum, Saira
Format: Article
Language:English
Subjects:
Acquired immune deficiency syndrome
AIDS
Analysis
Business competition
Calculus
COVID-19 vaccines
Disease prevention
Disease transmission
Epidemiology
existence and uniqueness
Fixed points (mathematics)
Forecasts and trends
Fractal analysis
Fractal geometry
fractal-fractional derivative
Fractals
fractional Adams-Bashforth method
Fractional calculus
Functional analysis
Health aspects
HIV
HIV (Viruses)
HIV model
Human immunodeficiency virus
Immune system
Infection
Infections
Mathematical models
numerical simulation
Population
Qualitative analysis
Simulation
Simulation methods
Stability
Ulam-Hyers stability
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Summary:This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8050299