The number of reported early syphilis cases in San Francisco has increased steadily since 2005. It is not yet clear what factors are responsible for such an increase. A recent analysis of the sexual contact network of men who have sex with men with syphilis in San Francisco has discovered a large connected component, members of which have a significantly higher chance of syphilis and HIV compared to non-member individuals. This study investigates whether it is possible to exploit the existence of the largest connected component to design new notification strategies that can potentially contribute to reducing the number of cases. We develop a model capable of incorporating multiple types of notification strategies and compare the corresponding incidence of syphilis. Through extensive simulations, we show that notifying the community of the infection state of few central nodes appears to be the most effective approach, balancing the cost of notification and the reduction of syphilis incidence. Additionally, among the different measures of centrality, the eigenvector centrality reveals to be the best to reduce the incidence in the long term as long as the number of missing links (non-disclosed contacts) is not very large

The work of J.S. and D.J. has been partially supported by the research grants MTM2014-52402-C3-3-P of the Spanish Government (MINECO) and MPCUdG2016/047 of the Universitat de Girona. J.S. and D.J. are members of the research groups 2014SGR-1083 and 2014SGR-555 of the Generalitat de Catalunya, respectively