A spatially varying differential equation for multi-patch pandemic propagation
Mesoscale and Nanoscale Physics
2025-02-04 v1 Statistical Mechanics
Abstract
We develop an extension of the Susceptible-Infected-Recovery (SIR) model to account for spatial variations in population as well as infection and recovery parameters. The equations are derived by taking the continuum limit of discrete interacting patches, and results in a diffusion equation with some nonlinear terms. The resulting population dynamics can be reinterpreted as a nonlinear heat flow equation where the temperature vector captures both infected and recovered populations across multiple patches.
Keywords
Cite
@article{arxiv.2502.00454,
title = {A spatially varying differential equation for multi-patch pandemic propagation},
author = {Abhimanyu Ghosh},
journal= {arXiv preprint arXiv:2502.00454},
year = {2025}
}