Epidemics on adaptive networks

The real world has abundant examples of complex networks, from the world wide web to human social networks to neurons in the brain. Many of these networks evolve over time, forming new connections and breaking old ones. At the same time, the nodes of the network may themselves display complicated dynamics. We are interested in adaptive networks, where the network geometry responds to the state of the nodes, while at the same time the nodes are affected by the network geometry. That is, dynamics of the network and dynamics on the network are interrelated.

Degree distributions when a network is rewired adaptively. Infectives have fewer neighbors, as non-infected people move away from them.
Of particular interest is the problem of epidemic spreading on an adaptive network. Human social interactions may be considered as a network, but these interactions are not fixed. People may change their behavior if they know that a disease is spreading within their community. For example, people who are not ill may choose to break off contact with friends who are sick to avoid catching the disease. This system may be modeled as an adaptive network. Changing the links adaptively has an impact both on the structure of the network and on the progress of the epidemic, for example whether the disease dies out or persists within the population.

The study of adaptive networks is a relatively new field, and researchers are still developing tools to understand such systems. Adaptive networks display a rich dynamics that brings models a step closer to accurately reflecting real world phenomena.