### AIMS Mathematics

2019, Issue 4: 1145-1169. doi: 10.3934/math.2019.4.1145
Research article Topical Sections

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

• Received: 26 May 2019 Accepted: 23 July 2019 Published: 19 August 2019
• MSC : 34A34, 34C60, 92B05

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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