Social Networks | Week 10

Social Networks Week 10 Assignment 10 Answers

Course Link: Social Networks | Week 10

Q1. Consider the example of Book sales for the power law distribution where we plot a graph between the popularity of the book and sales. We observe the top ranked books have high sales and the low ranked books have very low sales. Assuming that Best seller books constitute 20 percent of sales, which of the following is true?
Selling only Best seller books is profitable
Selling niche books is will be a loss
Selling both Best sellers and Niche books is profitable
all of the above

Q2. Consider a tree structures network where every node has 5 children and the probability of a node infecting the other is 0.8. Calculate the number of child nodes infected by a single node at level 1.
5
4
3
2

Q3. Consider a branching model of network where every node has 5 children and the probability of transmission of an infection is 0.4, what is the probable number of people infected at level 4?
24
16
20
5

Q4. Which of the following is true for Basic reproductive number?
It is the number of people infected by a single infected person
It is the number of people with ample immunity to an infection
It is the number of people who can recover from an infection
It is the probability of disease transmission

Q5. In a SIS model, if probability of spreading disease is 1/3, what will be the probability that a person who recovered from the disease is likely to get infected again?
0
1
1/3
2/3

Q6. Consider a disease ‘A’. People who are diagnosed in the earlier stage have high chance of recovery. But the intense infection of ‘X’ will lead to death. The recovered people also do not stand a chance to get infected again. What kind of model does this disease ‘X’ exhibit?
SIR
SIS
Both SIR and SIS
Neither SIR nor SIS

Q7. In the percolation model (static view of the SIR model), assume that TI=1. For every edge Eu,v
in the network, we toss a biased coin which shows head with a probability of p, which is the infection rate of the disease, i.e., the probability that v will become infected in the next iteration, given that u is infected. If head turns up, we assume an edge to be open, else blocked. According to this percolation model, a node w in the network will become infected
if there is a path consisting of blocked edges from any of the initially infected nodes to w.
if there is a path consisting of open edges from any of the initially infected nodes to w.
if there is a path from any of the initially infected nodes to w. The path may consist of any edgesopen/ blocked.
if there does not exist any path from any of the initially infected nodes to w.

Q8. In a branching model, Basic reproductive number helps to identify if a disease will be an epidemic or not. Which of the following statements is/are true?
Statement I – If R0<1, then the disease dies out from the network with a probability 1
Statement II – If R0>1, then the disease persists in the network with a probability greater than 0.
I only
II only
Both I and II
None

Q9. Suppose the basic reproductive number is estimated to be R0=1.2. If a vaccine giving 100% immunity is available next time and a fraction v = 0.4 of randomly selected individuals were vaccinated, an estimate of the new reproductive number would be
3
0.72
0.48
1

Q10. Given that the Reproductive number of an epidemic in action is 1.2. What are valid attempts to curb the disease or reduce the reproductive number?
Isolate the infected person so that we reduce the number of people getting infected.
Create awareness among the population to follow proper hygiene thereby reducing the probability of the disease spread
susceptible people visiting public gatherings to reduce contact probability with infected persons
Vaccinating to gain immunity against the infection