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An In Vitro Model for Measuring Immune Responses to Malaria in the Context of HIV Co-infection

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A Network Immuno-Epidemiological HIV Model.

Churni Gupta¹, Necibe Tuncer², Maia Martcheva³

¹Department of Mathematics, University of Florida, Gainesville, USA. churnibidisha@ufl.edu.

Bulletin of Mathematical Biology

|January 16, 2021

Summary

This summary is machine-generated.

This study introduces a complex network model for HIV, revealing how network size impacts disease spread. The number of infected individuals shows a varied relationship with within-host factors depending on network structure.

Keywords:

Age structured Basic reproduction number Epidemic model HIV Network

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Chronic, Acute, and Reactivated HIV Infection in Humanized Immunodeficient Mouse Models

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Published on: December 3, 2019

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.