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

1 Laboratoire de Mathématiques Appliquées du Havre, Normandie Université, FR CNRS 3335, ISCN, 76600 Le Havre, France
2 Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Topical Section: Mathematical modeling

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.
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Keywords complex network; epidemiological model; basic reproduction number; graph topology; HIV/AIDS; Cape Verde

Citation: Guillaume Cantin, Cristiana J. Silva. Influence of the topology on the dynamics of a complex network of HIV/AIDS epidemic models. AIMS Mathematics, 2019, 4(4): 1145-1169. doi: 10.3934/math.2019.4.1145


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