Immunization against Network-pox

Unicamp has been plagued by a persistent, annual outbreak of a highly contagious but rarely fatal disease called Network-pox. Network-pox is an SIS-like pathogen (Susceptible-Infected-Susceptible) in which recovery from symptoms (a dangerous aversion to studying network science) confers only temporary immunity, so students quickly become susceptible again.

The typical university population forms a highly heterogeneous contact network, where some students attend every lecture, participate in multiple clubs, forming large hubs, but others occasionally attend classes, study in their rooms, and have limited social interaction.

Thankfully, Prof. Meidanis has found a cure for the Network-pox, the MO412 Vaccine, leading to a mass vaccination program, successfully immunizing 92% of the students at Unicamp at random. However, the question of whether the disease has been eradicated remains unsolved.

A previous study has revealed that the Unicamp network was scale-free, with moments $\langle k \rangle = 5$ and $\langle k^2 \rangle = 200$.

Which of the following statements can be made about Network-pox's spreading rate and eradication?

a) Network-pox was certainly eradicated, despite being highly contagious, with a spreading rate of at least 0.4

b) Network-pox was certainly eradicated, and the estimated spreading rate is, at most, 0.3.

c) Network-pox was certainly not eradicated because the spreading rate was under 0.5.

d) Network-pox was certainly not eradicated, as the spreading rate was estimated to be at least 0.2

e) None of the above


Original Idea: Daniel Gardin


Comments

  1. Joao MeidanisNovember 29, 2025 at 9:17 AM

    Questão muito interessante, mas creio que possa estar havendo uma confusão entre 'spreading rate' e 'epidemic threshold'. Não vejo como derivar o 'spreading rate' a partir das informações dadas, mas dá para saber o 'epidemic threshold'.

    ReplyDelete
    Replies
    1. DanielNovember 29, 2025 at 12:46 PM

      Não é possível derivar a spreading rate, ela é um grau de liberdade na questão.
      A ideia é verificar se a combinação de: foi ou não erradicada + possível valor de spreading rate pode ter acontecido de fato, dadas as estatísticas e que 92% dos estudantes foram vacinados.

      Delete

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