The most common friend first immunization**Project supported by the National Natural Science Foundation of China (Grant No. 61263019), the Program for International Science and Technology Cooperation Projects of Gansu Province, China (Grant No. 144WCGA166), and the Program for Longyuan Young Innovation Talents and the Doctoral Foundation of Lanzhou University of Technology, China.

Abstract

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.