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Ecological and eco-social network models were constructed with different levels of complexity in order to represent and evaluate management strategies for controlling the alien species Pterois volitans in Chinchorro bank (Mexican Caribbean). Levins´s loop analysis was used as a methodological framework for assessing the local stability (considered as a component of sustainability) of the modeled management interventions represented by various scenarios. The results provided by models of different complexity (models 1 through 4) showed that a reduction of coral species cover would drive the system to unstable states. In the absence of the alien lionfish, the simultaneous fishing of large benthic epifaunal species, adult herbivorous fish and adult carnivorous fish could be sustainable only if the coral species present high levels of cover (models 2 and 3). Once the lionfish is added to the simulations (models 4 and 5), the analysis suggests that although the exploitation or removal of lionfish from shallow waters may be locally stable, it remains necessary to implement additional and concurrent human interventions that increase the holistic sustainability of the control strategy. The supplementary interventions would require the implementation of programs for: (1) the restoration of corals for increasing their cover, (2) the exploitation or removal of lionfish from deeper waters (decreasing the chance of source/sink meta-population dynamics) and (3) the implementation of bans and re-stocking programs for carnivorous fishes (such as grouper) that increase the predation and competition pressure on lionfish (i.e. biological control). An effective control management for the alien lionfish at Chinchorro bank should not be optimized for a single action plan: instead, we should investigate the concurrent implementation of multiple strategies.