Week 7: simple and complex contagion

Question 1

What are strong ties?

Answer 1

Family, partner, close friends, core discussion network. Usually located within the closed triangles in a network

Question 2

What are weak ties?

Answer 2

Distant friends, neighbours, colleagues - interact with less frequently, less invested in relationship

Question 3

What is simple contagion?

Answer 3

Single contact is sufficient for transmission, the strength of weak ties

Question 4

What are examples of simple contagion?

Answer 4

Epidemic, rumours, job information

Question 5

How does diffusion in a social network work under simple contagion?

Answer 5

Two states of people. Inactivate: susceptible to a contagion. Activated: infected and can transmit the contagion to others
Virus is passed on with probability B

Question 6

How do weak ties help information spread in simple contagion?

Answer 6

Weak ties accelerate information diffusion. Under simple contagion a single tie between two communities can spread information between communities

Question 7

What is complex contagion?

Answer 7

Multiple and credible sources are required for transmission, the strength of strong ties

Question 8

What are examples of complex contagion?

Answer 8

Change of diet, high-risk social movements

Question 9

How does the redundancy of ties affect diffusion in simple and complex contagion?

Answer 9

Simple contagion: there is a lot of redundant information within the close community which is not efficient
Complex contagion: the redundancy of strong ties becomes useful

Question 10

What are bridge widths and how do they affect contagion?

Answer 10

The width of a bridge between two communities is defined as the number of overlapping ties between them. Complex contagion can only spread through wide bridges between communities

Question 11

What are the steps of the independent cascade model?

Answer 11

• Simple contagion
• Nodes can have two states: active (S=1) and inactive (S=0), once activated you cannot be inactive again
• At time t=0, k seed nodes are activated.
• When a node u is activated at time t, it has a single chance to activate each of its neighbours v at time t+1. The success depends on the probability p_uv assigned to the edge connecting u and v
• Stop when all the nodes are activated or the number of activated nodes is saturated

Question 12

What are the states of the SIR model?

Answer 12

-simple contagion
People in a network can have 3 states
- Susceptible (S): healthy people that can catch the virus with the contact of infected people, with certain probability B
- Infected (I): people who have been infected and are capable of infecting susceptible individuals (being infections within 1/gamma time steps)
- Recovered (R): people who have been infected and have either recovered from the disease and entered the removed compartment, or died

Question 13

What are the parameters in the SIR model?

Answer 13

B = transmission rate
Gamma = recovery rate
Virus strength = B/gamma

Question 14

What is the SEIR model for COVID?

Answer 14

Susceptible (S), exposed (infected but not yet infectious) (E), infectious (I), recovered (R)

• infectious person infects health person with probability π_infection
• after fixed number of steps T_exposure an exposed individual becomes infectious
• after becoming infectious recovery occurs with T_recovery steps

Question 15

What is the threshold model?

Answer 15

-complex contagion
To adopt a new behaviour an individual needs to be convinced by an absolute number or fraction of their social contacts
-acceptance probability p is a function of the absolute number of adopted peoples (ki) among node i’s neighbours

Question 16

What is the threshold model for collective behaviour?

Answer 16

If riot thresholds of individuals are 0,1,2,… there will be a domino effect

Question 17

What is the social tipping point?

Answer 17

The point at which innovation becomes self-sustaining, 16% of population

Question 18

What are the steps of the linear threshold model?

Answer 18

• A node has two states, active (Si=1) and inactive (Si=0), once activated will remain active all the time
• each node i has n direct neighbours
• each neighbour has a certain influence on node i defined as w_ij and ∑w_ji ≤ 1
• each node i has a fraction threshold 0 ≤ theta_i ≤ 1
• at each time step each inactivated note reviews the status of all its direct neighbours and will be activated if the weighted fraction of active neighbours exceeds the threshold