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July 11, 2026Communications on Pure and Applied MathematicsOpen Access

The SIR Model in a Moving Population: Propagation of Infection and Herd Immunity

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Authors

DDDuncan DauvergneASAllan Sly

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Overview

Modeling infection spread and herd immunity in moving populations, highlighting infection persistence and dynamics.

Key Points

  • This research aims to understand how an infection spreads in a moving population using SIR dynamics.
  • Analyzed infection spread through particles undergoing independent random walks.
  • Studied the transition of infection survival and the emergence of herd immunity.
  • Examined the coexistence of different infection phases around the infection front.
  • Infection can survive indefinitely with a positive probability when the infection rate is low.
  • Herd immunity arises with a density of recovered and susceptible particles, but no infected ones.
  • The model reveals both supercritical and subcritical phases around the infection front.

Cite This Study

Dauvergne et al. (2026) studied this question.

synapsesocial.com/papers/6a51dc79c18d7f28ca4ffaddhttps://doi.org/10.1002/cpa.70054
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