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arXiv · 2406.01822

Infection fronts in randomly varying transmission-rate media

Renzo Zagarra·Karina Laneri·Alejandro B. Kolton
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Abstract

We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that the critical average transmission rate for the steady-state propagation of the infection is overestimated by the naive mean-field homogenization. Furthermore, we observe that the velocity, profile, and harmfulness of the fronts, given a specific average transmission, are sensitive to the details of randomness. In particular, we find that the harmfulness of the front is larger the more uniform the transmission-rate is, suggesting potential optimization in vaccination strategies under constraints like fixed average-transmission-rates or limited vaccine resources. The large-scale geometry of the advancing fronts presents nevertheless robust universal features and, for a statistically isotropic and short-range correlated disorder, we get a roughness exponent $\alpha\approx 0.42 \pm 0.10$ and a dynamical exponent $z\approx 1.6 \pm 0.10$, which are roughly compatible with the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. We find that the KPZ term and the disorder-induced effective noise are present and have a kinematic origin.

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Renzo Zagarra, Karina Laneri, Alejandro B. Kolton. 2024-06-03. Infection fronts in randomly varying transmission-rate media. https://doi.org/10.1103/physreve.110.034308

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