Mathematical Analysis of Nonlinear Models in AIDS Transmission Dynamics

Abstract

This paper presents a comprehensive analysis of nonlinear mathematical models for HIV/AIDS epidemic transmission dynamics. We develop and analyze several deterministic compartmental models incorporating key epidemiological factors influencing HIV transmission, including variable infection rates, latency periods, and treatment interventions. Using differential equation systems, we establish the existence of disease-free and endemic equilibrium points and analyze their stability conditions through Lyapunov functions and the next-generation matrix approach. Basic reproduction numbers (R₀) are derived for each model to determine epidemic thresholds. Numerical simulations utilizing real epidemiological data from five distinct geographical regions validate our theoretical findings and demonstrate how intervention strategies affect disease trajectories. Sensitivity analysis reveals that behavioral interventions targeting transmission rates and early treatment initiation have the greatest impact on reducing R₀. Our findings contribute to the understanding of HIV/AIDS transmission dynamics and provide quantitative frameworks for evaluating the effectiveness of various intervention strategies in diverse epidemiological settings.