A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation...

Area of Science:

• Mathematical Biology
• Epidemiology
• Virology

Background:

• Human Immunodeficiency Virus (HIV) poses significant global economic and health challenges.
• Understanding HIV transmission dynamics is vital for effective control strategies.
• Mathematical models, particularly delay differential equations, are increasingly used to study complex biological systems.

Purpose of the Study:

• To develop a novel mathematical model for intramural HIV infection dynamics.
• To incorporate time delays representing viral entry and virion production.
• To analyze the stability of infection-free and endemic equilibrium states.

Main Methods:

• A system of delay differential equations was formulated to model HIV dynamics.
• The LaSalle invariance principle was applied to analyze the infection-free equilibrium.
• A higher-order accurate spectral scheme was employed for numerical simulations.

Main Results:

• The study proves that the disease-free equilibrium is locally and globally asymptotically stable when the reproduction number is less than unity.
• The model effectively captures the complex dynamics of intramural HIV infection.
• The spectral scheme ensures numerical accuracy and preserves essential properties of the continuous model.

Conclusions:

• The developed mathematical model provides a comprehensive understanding of HIV infection dynamics.
• The findings on equilibrium stability offer insights for potential intervention strategies.
• High-order numerical schemes are crucial for accurate simulation of delayed differential equation models in virology.