Breaking Apart Contact Networks with Vaccination

Infectious diseases can cause large disease outbreaks due to their transmission potential from one individual to the next. Vaccination is an effective way of cutting off possible chains of transmission, thereby mitigating the outbreak potential of a disease in a population. From a contact network perspective, vaccination effectively removes nodes from the network, thereby breaking apart the contact network into a much smaller network of susceptible individuals on which the disease can spread. Here, we look at the continuum of small world networks to random networks, and find that vaccination breaks apart networks in ways that can dramatically influence the maximum outbreak size. In particular, after the removal of a constant number of nodes (representing vaccination coverage), the more clustered small world networks more readily fall apart into many disjoint and small susceptible sub-networks, thus preventing large outbreaks, while more random networks remain largely connected even after node removal through vaccination. We further develop a model of social mixing that moves small world networks closer to the random regime, thereby facilitating larger disease outbreaks after vaccination. Our results show that even when vaccination is entirely random, social mixing can lead to contact network structures that strongly influence outbreak sizes. We find the largest effects to be in the regime of relatively high vaccination coverages of around 80%, where despite vaccination being random, outbreak sizes can vary by a factor of 20.