Lucila G. Zuzek, Cristian E. La Rocca, Lidia A. Braunstein, Jose Roberto Iglesias<\strong>
Some doubts about the effects, beneficial or not, of vaccines arose in recent years. As a consequence some people decide to not vaccinate themselves and/or their relatives. This attitude in face of vaccines has clear consequences in the spread of diseases. In this paper we study, in a simultaneous way, the changes of opinions on vaccination together with the evolution of a disease that can become epidemic. To do so we consider a bi-layered complex network. One of the layers corresponds to a social network where people confront their opinions and influence the opinions of the others. This network may be of real or virtual contacts. The second layer corresponds to a network of physical contacts that can cause contagion of a disease. The dynamics of opinions makes use of a model where intermediate opinions are possible, and the evolution is such that with a given probability p opinions evolve towards extremes (In favor or against vaccination), while with probability 1-p opinions evolve to a middle term position1. The dynamics of contagion proceeds through the well-known SIR model. The results are sensitive to the ratio r=p/(1-p), to the infectivity of the disease and to the efficacy of the vaccine that we call W. Even though the results depend of the infectivity and on the ratio r, one observes that if the efficacy is lower than 80% opinion generally evolves against the vaccine, while for higher efficacy most of the populations decide to vaccinate.
 C.E. La Rocca, L.A. Braunstein, and F. Vazquez: The influence of persuasion in opinion formation and polarization. Europhys. Lett. 106 (2014) 40004.