Universal Behavior in a Generalized Model of Contagion
Physical Review Letters, 92 (21):
218701 (2004)Description
JL: Generic Contagion Model. Discrete state S I R At each time step: Each individual meets another randomly picked If the other is infected then with prob p get a dose of size from pdf_d Agent collect (sum) doses of the last T meetings in D=sum(d(t)) If D > d* then an agent gets infected. Infection threshold d* from pdf_d* Introduces also recovery rate r (I->R) and resuspectible rate rho (R->S). For special case rho=r=1 (SIS) steadty state equation on the fraction of infected nodes, which is solvable by computation at arbitrary precision. Find that for a given T the model behavior depends only on P1 (=probability to get infected after 1 exposure) and P2 (probability to get infected after 2 exposures). Class I: Epidemic Threshold Models. P1>=P2/2. p_c marks the probabilty for which an initial seed is able to trigger an epidemic. Class II: Vanishing critical mass models. P2/2 > P1 >= 1/T. Have p_b < p_c for p>p_c same as epidemic, for p_b < p < p_c need a critical intial mass of infected nodes to trigger big epidemic. Class III: Pure critical mass models. 1/T > P1. No p_c<1 anymore.
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