2026-367

Consider the context of a disease spreading through a global network. Which of the following statements is false?

a) If a disease has different fatality rates depending on specific factors, such as COVID-19 being more dangerous for older people, then the best vaccination strategy for minimizing the number of deaths would be to prioritize high-risk groups. However, if the objective is to eradicate the disease, the best strategy would be to prioritize nodes with the highest number of links, since these nodes contribute more to disease transmission.

b) A disease with a very high fatality rate tends to be less likely to spread globally and become a pandemic, especially if infected individuals die before transmitting the disease to many others. In network terms, death removes a node from the transmission network, reducing the number of possible future infections.

c) If a vaccine exists and 90% of the population is vaccinated at random, the remaining 10% of unvaccinated individuals will not be affected at all by the existence of the vaccine.

d) Early identification of a disease, together with measures such as quarantine and social isolation, is one of the first and most important steps to prevent a local outbreak from becoming a pandemic.

e) None of the above is false.

Original idea by: Henrique Campos Padula

2026-366

The network below shows the contacts in a small population, modelled with the SI epidemic model.

Given a transmission rate β = 0.1, what is the characteristic time τ of the epidemic?

1. τ = 4
2. τ = 5
3. τ ≈ 2.86
4. τ = 0.5
5. None of the above

Original idea by: Gustavo P. C. P. da Luz

2026-365

How do assortative degree correlations typically influence the initial spread of a pathogen compared to neutral or disassortative networks?

1. They have no noticiable impact on epidemic dynamics, since the network scale regime influences the initial spread more than degree correlations.
2. They slow down the spread because hubs are disconnected from susceptible nodes.
3. They increase the epidemic threshold, making outbreaks less likely.
4. They accelerate the spread because highly connected nodes are more likely to be linked to other highly connected nodes.
5. None of the above.

Original idea by: Giuliano Macedo.

2026-364

A zombie infection spreads according to the SI model under the homogeneous mixing assumption. Researchers observe that faster zombies encounter healthy individuals more frequently, so the infection rate is proportional to the zombie walking speed:

$$\beta =c{v}_z,$$

where $v_z$ is the average zombie speed and $c$ is a proportionality constant.

A mutation doubles their average speed. The contact network remains unchanged, with

$$⟨k⟩=8$$

and

$$⟨k^2⟩=100.$$

According to the SI model on networks, by what factor does the characteristic time change after the mutation?

A) It is reduced by half.

B) It doubles.

C) It increases by a factor of four.

D) It remains unchanged.

E) None of the above.

Original idea by George Gigilas Junior

2026-363

Analyze the following statements about the impact of degree correlations on spreading phenomena in networks, and determine whether each statement is True (T) or False (F):

1. In the SIS model applied to scale-free networks whose second moment diverges, the epidemic threshold remains zero regardless its degree correlation (assortative, disassortative, or neutral).
2. Assortative correlation accelerates pathogen propagation because hubs, which are typically among the first nodes to become infected, preferentially connect to other hubs, facilitating rapid transmission through the most connected parts of the network.
3. In scale-free networks, a weakly infectious pathogen will always die out despite hubs existence, unlike random networks where the homogeneous connectivity allows the pathogen to spread steadily across the population.
4. In networks with finite second moment, disassortative correlations raise the epidemic threshold λ_c, making it harder for a pathogen to sustain itself in the network, while assortative correlations produce the opposite effect by lowering λ_c.

Choose the correct alternative:

A) T-T-T-F

B) F-T-F-T

C) T-T-F-T

D) T-F-T-T

E) None of the above

Original idea by: Gabriela Caspa

2026-362

Consider an epidemic spreading on a large scale-free network whose degree distribution follows

$$P(k) \sim k^{-\gamma}$$

with \(2 < \gamma < 3\). According to Network Epidemics theory field, which of the following statements is correct?

A) The epidemic spreads more slowly than in a random network because hubs act as bottlenecks.

B) In the SIS model, the epidemic threshold \(\lambda_c\) tends to zero as the network size becomes very large (\(N \to \infty\)).

C) The characteristic spreading time increases with the second moment \(\langle k^2 \rangle\).

D) The early-time behavior of the SI model is linear in time rather than exponential.

E) None of the above.

Original idea by: Carlos Trindade

2026-361

Given a network with a defined community division, which has positive modularity, choose the correct alternative:

a) Applying a degree-preserving exchange where two inter-community edges are removed and two intra-community edges are created will increase the modularity.

b) Merging two different communities into one will increase the modularity.

c) Removing an edge between nodes in different communities will increase the modularity.

d) Adding an intra-community edge to the network will necessarily increase the modularity.

e) None of the above.

Original idea by: João Pedro Carolino Morais