Chapter 13 Disease Spreading in Time-Evolving Networked Communities

Human communities are organized in complex webs of contacts that may be represented by a graph or network. In this graph, vertices identify individuals and edges establish the existence of some type of relations between them. In real communities, the possible edges may be active or not for variable periods of time. These so-called temporal networks typically result from an endogenous social dynamics, usually coupled to the process under study taking place in the community. For instance, disease spreading may be affected by local information that makes individuals aware of the health status of their social contacts, allowing them to reconsider maintaining or not their social contacts. Here we investigate the impact of such a dynamical network structure on disease dynamics, where infection occurs along the edges of the network. To this end, we define an endogenous network dynamics coupled with disease spreading. We show that the effective infectiousness of a disease taking place along the edges of this temporal network depends on the population size, the number of infected individuals in the population and the capacity of healthy individuals to sever contacts with the infected, ultimately dictated by availability of information regarding each individual’s health status. Importantly, we also show how dynamical networks strongly decrease the average time required to eradicate a disease. J.M. Pacheco (!) Centro de Biologia Molecular e Ambiental, Universidade do Minho, 4710 057, Braga, Portugal Departamento de Matemática e Aplicações, Universidade do Minho, 4710 057, Braga, Portugal ATP-group, P-2744-016, Porto Salvo, Portugal e-mail: jmpacheco@math.uminho.pt S. Van Segbroeck ATP-group, P-2744-016, Porto Salvo, Portugal F.C. Santos ATP-group, P-2744-016, Porto Salvo, Portugal INESC-ID & Instituto Superior Técnico, Universidade de Lisboa, 2744-016, Porto Salvo, Portugal © Springer Nature Singapore Pte Ltd. 2017 N. Masuda, P. Holme (eds.), Temporal Network Epidemiology, Theoretical Biology, DOI 10.1007/978-981-10-5287-3_13 291 292 J.M. Pacheco et al.