The SI and SIR epidemics on general networks
- Author(s): Aldous, D
- et al.
Published Web Locationhttps://doi.org/10.19195/0208-4220.127.116.11
© 2017, Wydawnictwo Uniwersytetu Wroclawskiego Sp. z o.o. All rights reserved. Intuitively one expects that for any plausible parametric epidemic model, there will be some region in parameter-space where the epidemic affects (with high probability) only a small proportion of a large population, another region where it affects (with high probability) a nonnegligible proportion, with a lower-dimensional “critical” interface. This dichotomy is certainly true in well-studied specific models, but we know of no very general results. A recent result stated for a bond percolation model can be restated as giving weak conditions under which the dichotomy holds for an SI epidemic model on arbitrary finite networks. This result suggests a conjecture for more complex and more realistic SIR epidemic models, and the purpose of this article** is to record the conjecture.