From Social to Epidemic Criticality and Back

In this paper, we study the spreading of epidemic in a network of individuals who may either contract a disease through contact with infected nearest neighbors or be vaccinated under the influence of neighbors who are already vaccinated. We show that both interaction between susceptible S and infected individuals I and the imitation of vaccination, a form of sociological interaction between susceptible S and vaccinated V individuals, may lead to a phase transition. If the spreading of epidemic is in the supercritical condition, corresponding to an unlimited growth of infection, the interaction between S and V must reach the supercritical condition to generate control of the spreading of infection, and bring the system to criticality. By adopting a theoretical perspective like that of multilayer complex networks, we study the case where the epidemiological network is under the influence of a sociological debate on whether to be vaccinated. We show that at criticality this debate generates clusters of individuals in favor of vaccination and clusters of individuals opposing it. 3 , 4 We study the influence of this debate on the spread of infection. We show that because of this debate in the epidemic network, a pattern emerges mirroring the structures of the sociological network. Finally, we introduce feedback of the epidemic network on the sociological network, and we prove that because of this feedback the sociological system undergoes a process of self-organization maintaining it at criticality. This system exhibits temporal complexity and critical slowing down. 1 We hope that these results may have an important effect of giving interesting suggestions to behavioral psychologists and information scientists actively involved in the analysis of the social debate on the moral issues connected to sexual activities.