## NPTEL Social Networks Week 10 Assignment Answers 2024

1. In the percolation model of the SIR epidemic model, a node in the network becomes infected if:

- There is a direct edge between the node and the initially infected node, regardless of its state
- The infection rate is greater than 0.5 for all edges in the network
- There exists a path of open edges from the initially infected node to the node in question
- The node has at least one neighbor that is not infected

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2. Which of the following correctly describes the behavior of a disease in a population based on the basic reproductive number, R_{0}?

- When R
_{0}< 1, every infected person infects less than one secondary person, and the disease persists with a high probability - When R
_{0}> 1, every infected person infects more than one secondary person, and the disease always dies away - When R
_{0 }< 1, the disease dies out with probability 1, since each infected person causes less than one secondary infection - When R
_{0}> 1, the disease persists in the network with a probability of 1

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3. Which of the following best represents the SIS (Susceptible-Infected-Susceptible) disease model

- Chickenpox, where people who recover gain lifelong immunity
- Common cold, where individuals can recover but remain susceptible to reinfection
- Measles, where recovery typically leads to permanent immunity
- Rabies, where infection usually leads to death without the possibility of reinfection

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4. If there exist a graph G, in which there are 10 nodes in level 1 and every node has 10 children then, number of nodes in 5^{th} level will be

- 50
- 5
^{10} - 10
^{5} - 10
^{10}

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5. Given the probability of spreading disease is 0.3, what is the probability that the same person is not infected for the second time?

- 0.3
- 0.7
- 1
- 0

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6. In an SIS model, if the probability of transmitting the disease is 0.4, what is the likelihood that an individual who has recovered will be reinfected?

- 0
- 0.4
- 0.6
- 1

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7. Consider the example of digital music streaming services, where we plot a graph between a song’s popularity and its number of streams, following a power law distribution. The most popular songs receive a significantly high number of streams, while lesser-known songs receive far fewer streams. Assuming that top-charting songs account for 30% of total streams, which of the following is true?

- Streaming only top-charting songs is profitable
- Streaming niche songs will lead to a loss
- Streaming both top-charting and niche songs is profitable
- None of the above

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8. If the basic reproductive number (R0) of contagion is greater than 1, meaning each infected individual, on average, infects more than one other person, which of the following strategies would be most effective in reducing the spread and curbing the contagion?

- Implementing widespread vaccination to increase immunity in the population
- Allowing large public gatherings to promote herd immunity through natural infection
- Reducing healthcare services to manage the number of new infections
- Ignoring the infection and focusing on treatment after symptoms appear

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9.

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10. In the given network K, each infected node has edges to two nodes in the next layer; since it infects each with probability 2/3, the expected number of new cases caused by a node is

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