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Infection fronts in randomly varying transmission-rate media
Renzo Zagarra1, Karina Laneri2, Alejandro B Kolton2
1Centro Atómico Bariloche and Instituto Balseiro, <a href="https://ror.org/01xz39a70">CNEA</a>, Universidad Nacional de Cuyo, 8400 Bariloche, Argentina.
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 α≈0.42±0.10 and a dynamical exponent z≈1.6±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.
Insights
This study reveals that infection front propagation in spatial SIR models is sensitive to transmission rate randomness. Uniform transmission increases front harmfulness, impacting vaccination strategies and revealing universal geometric features compatible with KPZ universality.
Area of Science:
- Epidemiology
- Statistical Physics
- Computational Biology
Background:
- The spatial SIR model is crucial for understanding infectious disease dynamics.
- Quenched random transmission rates introduce complex behaviors in infection spread.
- Mean-field homogenization often overestimates critical transmission rates.
Purpose of the Study:
- To numerically investigate infection front geometry and transport in a 2D spatial SIR model.
- To analyze the impact of short-range correlated quenched random transmission rates.
- To compare findings with theoretical models like Kardar-Parisi-Zhang (KPZ).
Main Methods:
- Numerical simulations of the spatial SIR model in two dimensions.
- Incorporation of short-range correlated quenched random transmission rates.
- Analysis of infection front velocity, profile, and harmfulness.
Main Results:
- Critical transmission rate for steady-state propagation is overestimated by naive mean-field homogenization.
- Front velocity, profile, and harmfulness depend on randomness details.
- Higher uniformity in transmission rates leads to increased front harmfulness.
- Front geometry exhibits universal features, with roughness exponent α≈0.42±0.10 and dynamical exponent z≈1.6±0.10.
- KPZ term and disorder-induced noise are present with kinematic origin.
Conclusions:
- Randomness in transmission rates significantly affects infection spread dynamics.
- Uniformity in transmission can enhance disease spread, informing vaccination strategies.
- The observed front dynamics align with the 1D KPZ universality class, suggesting robust universal behaviors.
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