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Some epidemics have been empirically observed to exhibit outbreaks of allpossible sizes, i.e., to be scalefree or scale-invariant. Differentexplanations for this finding have been put forward; among them there is amodel for "accidental pathogens" which leads to power-law distributed outbreakswithout apparent need of parameter fine tuning. This model has been claimed tobe related to self-organized criticality, and its critical properties have beenconjectured to be related to directed percolation. Instead, we show that thisis a (quasi) neutral model, analogous to those used in Population Genetics andEcology, with the same critical behavior as the voter-model, i.e. the theory ofaccidental pathogens is a (quasi)-neutral theory. This analogy allows us toexplain all the system phenomenology, including generic scale invariance andthe associated scaling exponents, in a parsimonious and simple way.

Quasi-Neutral theory of epidemic outbreaks