"

Social Network Analysis: Epidemics

QUESTION 1

Consider two versions of the primary school network: one that includes only edges with weights greater than or equal to the median value of the original graph (call this network A), and another in which you include only edges with weights greater than or equal to the meanvalue of the original graph (call this network B). Set the transmission probability (p.t argument) to 0.05 in each case, and run the simulation for 100 rounds. Do this about ten times to get a sense of the amount of variation in the results. Which of the following statements are true:

	A.	Full infection of the network is typically reached in both networks A and B, in fewer than 80 rounds.
	B.	In both cases, full infection of the network is usually not reached until after the round 80 (i.e. between rounds 80 and 100).
	C.	By round 100, fewer than half the nodes are typically infected in network A, while more than half thenodes are typically infected in network B.
	D.	For network A, full infection of the network is usually reached after round 80; whereas this happens in fewer than 50 rounds for network B.
	E.	None of the above.

QUESTION 2

Consider network A of the primary school network described in #1, which includes only edges greater than or equal to the median value. This time, please compare the results of simulations in which transmission probability is set to 0.005 (simulation A) with results with the same parameter set to 0.001 (simulation B). Run each simulation for 200 rounds, as before.

	A.	Both simulations A and B show full infection of the network by 100 rounds.
	B.	Simulation A typically reaches full infection before 50 rounds, while simulation B reaches full infection after 50 rounds (i.e. between rounds 50 and 200).
	C.	Simulation B typically reaches full infection before 50 rounds, while simulation A reaches full infection after 50 rounds (i.e. between rounds 50 and 200).
	D.	Simulation A typically reaches full infection between 50 and 150 rounds, while simulation B shows between 50 to 75% of nodes infected by 100 rounds.
	E.	Simulation A typically reaches full infection between 50 and 150 rounds, while simulation B shows less than 50% of nodes infected by 100 rounds.

QUESTION 3

Create two versions of the Barabasi preferential attachment network with 90 nodes, and with number of new edges in each step of network growth set at m=1 (for network A) and m = 2 (for network B). For both versions of this 90-node network, set power=0.98. The settings for networks A and B are already included in the R script file that comes with this lab. Run simulations for 100 rounds, with probability of transmission set at 0.05. Which of the following is true:

	A.	Network A typically reaches full infection within the first 90 rounds.
	B.	Network B typically reaches full infection within the first 90 rounds.
	C.	For network A, the simulation after 100 rounds often ends in infection in less than half of the nodes.
	D.	For network B, the simulation after 100 rounds often ends in infection in less than half of the nodes.
	E.	B and C only.

QUESTION 4

Create three versions of the 1-dimensional Watts-Strogatz small-worlds networks with 50 nodes; with each node's probability rewiring set at p=0.01 (network A), p=0.1 (network B), and p=0.2 (network C). These settings are included in the R script that comes with this lab (and commented accordingly). Run simulations for 200 rounds, with probability of transmission set at 0.05. Which of the following is true:

	A.	Network A typically does not typically reach full infection untilbetween 100 and 200 rounds.
	B.	Network B typically does not typically reachfull infectionuntilbetween 100 and 200 rounds.
	C.	Network C typically does not typically reachfull infectionuntil 100 and 200 rounds.
	D.	All of the above.
	E.	None of the above.

QUESTION 5

Create two versions of the Erdos-Renyi graph consisting of 75 nodes: One in which the average degree is the logarithm of the number of nodes (network A), and another version of the network with half the number of edges as network A (call this network B). Run simulations for 100 rounds, with probability of transmission set at 0.05. Which of the following is true:

	A.	Network A is likely to reach full infection, in less than 60 rounds.
	B.	Network B is likely to reach full infection, in less than 60 rounds.
	C.	Network A is likely to be fully connected.
	D.	Network B is likely to be fully connected.
	E.	A and C only.

QUESTION 6

The primary school network has 238 nodes. Compare version B of this network described in question 1 (includes edges with weights at least as large as the mean value), to three theoretical model networks with the same number of nodes (238), although the number of edges may vary: a) Erdos-Renyi graph with average degree as the logarithm of the number of nodes, like network A of question; b) Barabasi preferential attachment with m=2 and power=0.98, like network B from question 3; c) Watts-Strogatz small-worlds network with p=0.1, like network B from question 4. Run simulations with 100 rounds, with transmission probability 0.05. Which of the following statements is true about the primary school network in its comparison to the three theoretical models? Please make sure that each simulated network has 238 nodes like the primary school network. As always, you need to run the simulations multiple times to get a feel for the patterns.

	A.	Full infection tends to occur before the Erdos-Renyi random network.
	B.	Full infection tends to occur before the Barabasi preferential attachment network.
	C.	Full infection tends to occur before the Watts-Strogatz small-worlds network.
	D.	Among all four models, full infection is least likely to occur for the Watts-Strogatz small-worlds network.
	E.	All of the above

"