Heterogeneous diffusion with recruitment and mortality
Abstract
We study a heterogeneous diffusion process with a position-dependent diffusion coefficient in the presence of independent recruitment and mortality. This framework generalises heterogeneous diffusion under stochastic resetting, which is recovered as the special case of equal recruitment and mortality rates. At long times, the system approaches a non-equilibrium stationary state with a mean squared displacement that saturates to a value independent of the recruitment rate. Crucially, this saturation limit directly encodes the underlying transport regime via an effective exponent applied to the diffusion coefficient, and we characterise the non-trivial transition to this stationary regime. We further derive the mean first-passage time to a target and show that, for a fixed recruitment-to-mortality ratio, an optimal mortality rate minimises the search time. This "mortality-assisted search" effect is confirmed by numerical evaluation. Reinterpreting recruitment and mortality as infection and removal processes, we apply the model to epidemic spreading and show that a moderate removal rate can counter-intuitively accelerate, rather than delay, the arrival of infection at a new spatial region. Beyond epidemiology, our framework offers broad relevance to systems featuring concurrent particle creation and destruction, such as bacterial growth, tracer diffusion in reactive fluids, or cellular population dynamics in crowded environments.
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BibTeX
@misc{gutierrez2026heterogeneous,
title = {{Heterogeneous diffusion with recruitment and mortality}},
author = {Esther D Gutiérrez and Alexander López and R K Singh and Sébastien Fumeron and Malte Henkel and Trifce Sandev},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08022},
eprint = {2610.08022},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05780673v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Heterogeneous diffusion with recruitment and mortality
AU - Esther D Gutiérrez
AU - Alexander López
AU - R K Singh
AU - Sébastien Fumeron
AU - Malte Henkel
AU - Trifce Sandev
PY - 2026
DA - 2026/10/06
PB - HAL
DO - 10.48550/arxiv.2610.08022
UR - https://hal.science/hal-05780673v1
AB - We study a heterogeneous diffusion process with a position-dependent diffusion coefficient in the presence of independent recruitment and mortality. This framework generalises heterogeneous diffusion under stochastic resetting, which is recovered as the special case of equal recruitment and mortality rates. At long times, the system approaches a non-equilibrium stationary state with a mean squared displacement that saturates to a value independent of the recruitment rate. Crucially, this saturation limit directly encodes the underlying transport regime via an effective exponent applied to the diffusion coefficient, and we characterise the non-trivial transition to this stationary regime. We further derive the mean first-passage time to a target and show that, for a fixed recruitment-to-mortality ratio, an optimal mortality rate minimises the search time. This "mortality-assisted search" effect is confirmed by numerical evaluation. Reinterpreting recruitment and mortality as infection and removal processes, we apply the model to epidemic spreading and show that a moderate removal rate can counter-intuitively accelerate, rather than delay, the arrival of infection at a new spatial region. Beyond epidemiology, our framework offers broad relevance to systems featuring concurrent particle creation and destruction, such as bacterial growth, tracer diffusion in reactive fluids, or cellular population dynamics in crowded environments.
ER -