A Network Immuno-Epidemiological HIV Model

Area of Science:

• Mathematical modeling
• Epidemiology
• Immunology

Background:

• Human Immunodeficiency Virus (HIV) presents a complex challenge for epidemiological modeling.
• Understanding disease dynamics on complex networks is crucial for effective intervention strategies.

Purpose of the Study:

• To formulate and analyze a multi-scale nested immuno-epidemiological model for HIV transmission on complex networks.
• To establish the mathematical well-posedness of the proposed model.
• To investigate the impact of network structure and within-host dynamics on HIV prevalence.

Main Methods:

• Development of a mathematical model using coupled ordinary differential equations and a partial differential equation.
• Proof of existence, uniqueness, and well-posedness for the immunological and multi-scale models.
• Derivation of the basic reproduction number ([Formula: see text]) for the immuno-epidemiological system.
• Numerical simulations to explore model behavior under varying network conditions.

Main Results:

• The disease-free equilibrium is globally stable when [Formula: see text] and unstable when [Formula: see text].
• Numerical simulations indicate that the basic reproduction number ([Formula: see text]) increases with the number of nodes in the network.
• For scale-free networks, infected individuals at equilibrium exhibit a hump-like relationship with the within-host reproduction number, which shifts to a monotone relationship in networks with predominantly low or high connectivity nodes.

Conclusions:

• The study provides a robust mathematical framework for understanding HIV dynamics on complex networks.
• Network topology significantly influences HIV transmission and equilibrium prevalence.
• Intervention strategies may need to be tailored based on network characteristics and within-host viral factors.