Introduction to the Modeling and Analysis of Complex Systems

16.4. SIMULATING ADAPTIVE NETWORKS 361• Epidemiological networks. The nodes are the individuals and the edges are thephysical contacts among them. The node states include their pathologic states(healthy or sick, infectious or not, etc.), which are coupled with topological changescaused by death, quarantine, and behavioral changes of those individuals.• Evolution of social communities. The nodes are the individuals and the edges aresocial relationships, conversations, and/or collaborations. The node states includesocio-cultural states, political opinions, wealth, and other social properties of thoseindividuals, which are coupled with topological changes caused by the people’s entryinto or withdrawal from the community, as well as their behavioral changes.In these adaptive networks, state transitions of each node and topological transformationof networks are deeply coupled with each other, which could produce characteristicbehaviors that are not found in other forms of dynamical network models. As I mentionedearlier in this chapter, I am one of the proponents of this topic [66], so you shouldprobably take what I say with a pinch of salt. But I firmly believe that modeling and predictingstate-topology co-evolution of adaptive networks has become one of the majorcritical challenges in complex network research, especially because of the continual floodof temporal network data [65] that researchers are facing today.The field of adaptive network research is still very young, and thus it is a bit challengingto select “well established” models as classic foundations of this research yet. Soinstead, I would like to show, with some concrete examples, how you can revise traditionaldynamical network models into adaptive ones. You will probably find it very easyand straightforward to introduce adaptive network dynamics. There is nothing difficult insimulating adaptive network models, and yet the resulting behaviors may be quite uniqueand different from those of traditional models. This is definitely one of those unexploredresearch areas where your open-minded creativity in model development will yield youmuch fruit.Adaptive epidemic model When you find out that one of your friends has caught aflu, you will probably not visit his or her room until he or she recovers from the illness.This means that human behavior, in response to the spread of illnesses, can change thetopology of social ties, which in turn will influence the pathways of disease propagation.This is an illustrative example of adaptive network dynamics, which we can implementinto the SIS model (Code 16.6) very easily. Here is the additional assumption we will addto the model:• When a susceptible node finds its neighbor is infected by the disease, it will severthe edge to the infected node with severance probability p s .