Work

A novel hybrid fractional approach to nonlinear dynamics of HIV transmission among men who have sex with men in Taiwan

Year: 2025

Type: article

Abstract: In Taiwan, human immunodeficiency virus (HIV) transmission occurs primarily among men who have sex with men (MSM). High-risk behaviors within this population contribute significantly to the variability and spread of the virus. This study introduces a fractional-order mathematical framework to better understand the dynamics of HIV transmission among MSM. We employ the modified Atangana-Baleanu derivative in the Caputo sense (ABC) to model the system. Theoretical analysis focuses on the existence, positivity, uniqueness, and sensitivity of solutions, utilizing the Leray-Schauder nonlinear alternative theorem and Banach's fixed-point theorem. Successive iterative sequences are constructed to verify the existence of solutions. Furthermore, we demonstrate the stability and uniqueness of the model solution within the Hyers-Ulam framework using tools from functional analysis. A chaos control method based on linear response regulation is applied to control the system dynamics and stabilize equilibrium points. Numerical simulations are conducted, and a graphical comparison between classical and fractional-order derivatives is presented using Lagrange interpolation within the modified ABC-fractional framework. Our findings highlight the significant impact of HIV transmission dynamics among MSM on public health systems. The modified ABC operator proves effective in capturing the long-term memory effects of the disease, enabling more precise and adaptive intervention strategies. This research provides policymakers and epidemic managers with a novel and robust modeling tool to develop more flexible and sustainable strategies for managing HIV spread, especially in light of evolving public health challenges.

Source: AIMS Mathematics

DOI: 10.3934/math.2025592

Authors: Sana Ullah Saqib, Ali Hasan, Yin-Tzer Shih

Institutions: National Chung Hsing University, Near East University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,200