Description
Figure 1.1
1. Let every node’s population be 1 (i.e., Ni = 1 for each i). Let β = 0.8 and γ = 0.5. Let
all initial infections be 0 except for node 1; node 1’s initial infection should be 0.01 (so
Ii(0) = 0.01 and Si(0) = 0.99 , but all other nodes have Si(0) = 1, Ii(0) = 0 and Ri(0) = 0).
What are the S, I, and R quantities after 1 time step?
2. How many time steps would it take before someone is infected in every node?
3. Suppose that the connection between node 2 and node 1 is removed. If nothing else changes
in the network, would this change the spread of the epidemic? Can you predict how many
people in node 2 would eventually get sick?
4. Repeat that same thought experiment, but this time let the initial infection start on node
2 (so I2(0) = 0.01 and S2(0) = 0.99, but all other nodes have Si(0) = 1, Ii(0) = 0 and
Ri(0) = 0). Now can you predict how many people in node 2 would eventually get sick?
5. Instead, suppose you remove the connection from node 2 to node 1, and replace it with a
self-loop on 2 with weight 1. If nothing else changes in the network (and the infection starts
at node 1), would this change the spread of the epidemic? Can you predict how many people
in node 2 would eventually get sick?