2021-070

Consider a disease infecting a population with \( N \) individuals, where \( S(t) \) is the number of individuals that are healthy (susceptible to the disease) at time \( t \), \( I(t) \) is the number of individuals that have been already infected at time \( t \), \( \langle k \rangle \) is the number of contacts that an individual usually has, and \( \beta \) is the rate of transmission.

Under the homogeneous mixing hypothesis, what is the probability that an infected person encounters a healthy individual?

1. \( S(t)I(t) \)
2. \( S(t)/N \)
3. \( I(t)/N \)
4. \( \beta \langle k \rangle S(t) I(t) / N \)
5. None of the above

Original idea by: Leandro Stival

2021-069

Regarding epidemic forecasting, it is correct to state that:

1. the relative times of disease arrival depend only on the degree distribution of the mobility network.
2. the relative times of disease arrival depend only on the clustering coefficients of the mobility network.
3. the relative times of disease arrival depend only on the topology of the mobility network.
4. It is not possible to predict the times of disease arrival just by looking at the mobility network.
5. None of the above.

Original idea by: Sara Mercês

2021-068

Given the two networks (each with 3 different colored partitions) shown in the image below:

1                                           2

Which of the networks has the smallest modularity? What is this value, rounded to two decimal places?

1. Network 1, M = 0.49
2. Network 1: M = 0.41
3. Network 2: M = 0.49
4. Network 2: M = 0.41
5. None of the above

Original idea by: Victor Antonio Menuzzo

2021-067

Suppose that there is a viral epidemic following a classic SIR model in a certain region. What would be the effect of lockdown in this region?

1. It increases the value of \( R_0 \)
2. It reduces the value of the recovery rate, which reduces \( R_0 \)
3. It reduces the average degree, moving out from endemic state
4. It does not affect the current epidemic state
5. None of the above

Original idea by: Matheus Cerqueira