Solution of an infection model near threshold

Abstract

We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the problem to the first passage time of a random walker subject to a drift that increases linearly with time. We recover the scaling results of Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales as $N^{2/3}$, with the average scaling as $N^{1/3}$, with an explicit form for the scaling function.

References in corpus (1)

• Size of Outbreaks Near the Epidemic Threshold

Cited by in corpus (2)

• Phase Transition with Non-Thermodynamic States in Reversible Polymerization
• Novel exponents control the quasi-deterministic limit of the extinction transition