Weird Way to update the Infection Status of SI model

[FeynmanDNA]

in ndlib/models/epidemics/SEISModel.py, in the commit https://github.com/GiulioRossetti/ndlib/commit/f80b1448db339fac6fa1cb63c093e714cd7add4a#diff-81ae80e5ab1d17420f19b47e51b93b8999cee1ad70db53e2aff5309ad3cd8899 the beta * num_infected_neighbors was changed into a 1 - (1-beta)**num_infected_neighbors.

I am wondering why was there such a change in the formula? The probability of beta should be linearly scaled with the number of infected neighbors right? Thanks for the hard work!

[FeynmanDNA]

Hi i went through the past issues and discovered that this beta vs num_infected_neighbors have been discussed before

But I kind of agree with https://github.com/GiulioRossetti/ndlib/issues/96#issuecomment-491229424 the beta is probability of getting the infection per I->S link right?

If we adopt the 1 - (1-beta)**num_infected_neighbors, then what is the definition of beta? thanks!

[GiulioRossetti]

It is not weird at all.

This is the probability of getting infected considering multiple independent contacts with infected individuals (each contact with prob beta of passing the infection).

[FeynmanDNA]

i see.

but is the previous approach linearly scaling the beta with num of infected neighbors wrong? Quite a number of publications use that calculation method, for example your 2018 publication "Diffusive Phenomena in Dynamic Networks: A Data-Driven Study":

[GiulioRossetti]

That's likely a typo.

Let's say that a linear scaling is not correct because it doesn't guarantee that the final probably value lies in [0,1]. Moreover, it doesn't model the independence of multiple infection sources.

[FeynmanDNA]

i see. thank you very much for the clarification!