  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.
