Introduction to the Modeling and Analysis of Complex Systems

364 CHAPTER 16. DYNAMICAL NETWORKS I: MODELINGBut if you try different parameter settings that would cause a pandemic in the originalSIS model (say, p i = 0.5, p r = 0.2), the effect of the adaptive edge removal is muchmore salient. Figure 16.13 shows a sample simulation result, where pandemic-causingparameter values (p i = 0.5, p r = 0.2) were used, but the edge severance probability p swas also set to 0.5. Initially, the disease spreads throughout the network, but adaptiveedge removal gradually removes edges from the network as an adaptive response to thepandemic, lowering the edge density and thus making it more and more difficult for thedisease to spread. Eventually, the disease is eradicated when the edge density of thenetwork hits a critical value below which the disease can no longer survive.Figure 16.13: Visual output of Code 16.15, with varied parameter settings (p i = 0.5,p r = 0.2, p s = 0.5). Time flows from left to right.Exercise 16.19 Conduct simulations of the adaptive SIS model on a random networkof a larger size with p i = 0.5 and p r = 0.2, while varying p s systematically.Determine the condition in which a pandemic will eventually be eradicated. Thentry the same simulation on different network topologies (e.g, small-world, scalefreenetworks) and compare the results.Exercise 16.20 Implement a similar edge removal rule in the voter model so thatan edge between two nodes that have opposite opinions can be removed probabilistically.Then conduct simulations with various edge severance probabilitiesto see how the consensus formation process is affected by the adaptive edge removal.