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 (2)

• Size of Outbreaks Near the Epidemic Threshold
• Moments of the first passage time under external driving

Cited by in corpus (11)

• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
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• Phase Transition with Non-Thermodynamic States in Reversible Polymerization
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• Epidemics with containment measures
• Outbreak size distributions in epidemics with multiple stages
• Critical behavior of the SIS epidemic model with time-dependent infection rate
• Scaling Behavior of Threshold Epidemics
• Robustness of correlated networks against propagating attacks
• Novel exponents control the quasi-deterministic limit of the extinction transition
• Epidemic Forecast Follies