The SIR Model in a Moving Population: Propagation of Infection and Herd Immunity
Abstract
ABSTRACT In a collection of particles performing independent random walks on we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and are removed at rate . We show that when is small, with positive probability the infection survives forever and grows linearly. Furthermore, after the infection reaches a region, it quickly passes through and leaves behind a herd immunity regime consisting of recovered particles, a small positive density of susceptible particles, and no infected particles. One notable feature of this model is the simultaneous existence of supercritical and subcritical phases on either side of an infection front of width.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
advanced mathematical theories
Publication details
- Journal / source
- Communications on Pure and Applied Mathematics
- Volume
- 79
- Issue
- 11
- Pages
- 2375–2429
- Publication date
- 8 July 2026
- Language
- EN