Influence of the topology on the dynamics of a complex network of HIV/AIDS epidemic models

TL;DR

This paper models HIV/AIDS spread in a heterogeneous geographical network, analyzing how network topology influences disease dynamics and identifying optimal structures to minimize infections.

Contribution

It introduces a novel complex network model for HIV/AIDS epidemiology, proving stability results and identifying optimal topologies for disease control.

Findings

Existence of a positively invariant region for the network solutions

Global asymptotic stability of the disease-free equilibrium

Identification of an optimal network topology to reduce infections

Abstract

In this paper, we propose an original complex network model for an epidemic problem in an heterogeneous geographical area. The complex network is constructed by coupling nonidentical instances of a HIV/AIDS epidemiological model for which a disease-free equilibrium and an endemic equilibrium can coexist. After proving the existence of a positively invariant region for the solutions of the complex network problem, we investigate the effect of the coupling on the dynamics of the network, and establish the existence of a unique disease-free equilibrium for the whole network, which is globally asymptotically stable. We prove the existence of an optimal topology that minimizes the level of infected individuals, and apply the theoretical results to the case of the Cape Verde archipelago.