Question about Spreading Phenomena

A research team is investigating the spread of a pathogen in a large contact network using an SIR model. During simulations, they obtained the following three observations:

  • Observation A: When β is increased while μ is kept fixed, the distribution of outbreak sizes shows a sudden transition from mostly small outbreaks to frequent large outbreaks.
  • Observation B: In networks with highly irregular degree distributions, a small fraction of nodes is responsible for the vast majority of early transmissions.
  • Observation C: After the outbreak peaks, the number of infectious nodes always decreases to zero, even when β ≫ μ. 

The team proposes the following four hypotheses to explain the observations:

  1. A corresponds to the existence of an epidemic threshold related to the transmissibility T = β/(β + μ).
  2. B indicates that heterogeneity in the degree distribution affects both the threshold condition and the probability of large outbreaks.
  3. C implies that the SIR model can exhibit a sustained endemic steady state when β is sufficiently large.
  4. A and B together suggest that the critical point for epidemic spreading depends on the ratio ⟨k²⟩ / ⟨k⟩.

Which set of hypotheses is consistent with all three observations?

A) Only 1 and 2.
B) Only 1, 2, and 3.
C) Only 1, 2, and 4.
D) Only 2, 3, and 4.
E) None of the above.


Original idea by: Mateus de Padua Vicente

Comentários

  1. Joao Meidanis29 de novembro de 2025 às 08:35

    Questão interessante, mas muito complexa. Em particular, a observação B parece fora da realidade, pois se os pesquisadores estão observando uma situação específica, como podem observar coisas a respeito de redes com distribuições irregulares em geral?

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