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Updated: Jul 1, 2025

Amplifying and Quantifying HIV-1 RNA in HIV Infected Individuals with Viral Loads Below the Limit of Detection by Standard Clinical Assays

Amplifying and Quantifying HIV-1 RNA in HIV Infected Individuals with Viral Loads Below the Limit of Detection by Standard Clinical Assays

Published on: September 26, 2011

Transmission dynamics of symptom-dependent HIV/AIDS models.

Wenshuang Li¹, Shaojian Cai², Xuanpei Zhai³

¹School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China.

Mathematical Biosciences and Engineering : MBE

|March 8, 2024

Summary

This study introduces two new mathematical models to understand HIV/AIDS dynamics in Fujian Province. The models analyze disease spread and stability, offering predictions for public health interventions.

Keywords:

HIV/AIDS extinction stability stationary distribution threshold

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Area of Science:

Epidemiology
Mathematical Modeling
Public Health

Background:

HIV/AIDS remains a significant public health concern globally and in specific regions like Fujian Province.
Understanding the dynamical properties of HIV/AIDS is crucial for effective control strategies.

Purpose of the Study:

To develop and analyze two novel, symptom-dependent mathematical models for HIV/AIDS.
To investigate the epidemiological dynamics and stability of HIV/AIDS in Fujian Province.
To provide predictions for HIV/AIDS prevalence using real-world data.

Main Methods:

Formulation of deterministic and stochastic, symptom-dependent HIV/AIDS models.
Analysis of model equilibria, including disease-free and endemic states.
Derivation of key epidemiological indicators (basic reproduction numbers).
Investigation of stationary distribution and stochastic extinction conditions.
Numerical simulations using surveillance data from Fujian.

Main Results:

The basic reproduction number was determined for the deterministic model.
Local and global stabilities of equilibrium points were established.
Stochastic indicators ($R_0^s$, $R_0^e$) were derived for the stochastic model.
Conditions for stationary distribution and stochastic extinction were identified.
Numerical simulations provided insights into current and future HIV/AIDS trends in Fujian.

Conclusions:

The developed models offer valuable tools for understanding HIV/AIDS transmission dynamics.
The study provides crucial insights into disease stability and extinction probabilities.
Findings support evidence-based public health planning for HIV/AIDS control in Fujian Province.