The most common friend first immunization

In this paper, a standard susceptible-infected-recovered-susceptible(SIRS) epidemic model based on the Watts–Strogatz(WS) small-world network model and the Barabsi–Albert(BA) scale-free network model is established, and a new immunization scheme — "the most common friend first immunization" is proposed, in which the most common friend's node is described as being the first immune on the second layer protection of complex networks. The propagation situations of three different immunization schemes — random immunization, high-risk immunization, and the most common friend first immunization are studied. At the same time, the dynamic behaviors are also studied on the WS small-world and the BA scale-free network. Moreover, the analytic and simulated results indicate that the immune effect of the most common friend first immunization is better than random immunization, but slightly worse than high-risk immunization. However,high-risk immunization still has some limitations. For example, it is difficult to accurately define who a direct neighbor in the life is. Compared with the traditional immunization strategies having some shortcomings, the most common friend first immunization is effective, and it is nicely consistent with the actual situation.     

This issue is dedicated to our friend and colleague Gilbert Grynberg

The Editors of this special issue and the partners of the QSTRUCT European Network are deeply saddened by the news of Gilbert Grynberg's departure. It was Gilbert's vision which first brought together specialists in optical and atomic physics to form the research field of quantum structures and to found the QSTRUCT Network. Within the Network, Gilbert worked tirelessly to promote collaboration and the exchange of new ideas. He was particularly popular with young researchers, who appreciated his eagerness to share ideas and who were inspired by his clarity of thought. It was Gilbert who first proposed a special issue of EPJ D dedicated to quantum structures. Sadly he will not see its publication. We remember a special scientist and educator, a colleague who was passionate about physics but brought his infectious sense of fun to all who worked with him. Even in the face of great hardships he remained a vibrant and enthusiastic member of our scientific family. We will all miss him.