A Novel Aggregated SIR Model for Spatial Epidemic Propagation

TL;DR

This paper introduces an extended SIR model that captures spatial epidemic spread across regions using aggregate variables, enabling analysis of complex outbreak patterns with fewer parameters.

Contribution

The novel model incorporates spatial effects into the classical SIR framework using aggregate compartments, avoiding high-dimensional network models.

Findings

Reproduces epidemic features like plateaus and multiple waves

Uses a small set of interpretable parameters

Provides a tractable analytical and numerical framework

Abstract

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture the dynamics of disease spread across multiple interconnected cities or populated regions, while avoiding the high dimensionality and large parameter sets typical of network based or agent-based approaches. Instead of explicitly modeling individual locations or mobility networks, we introduce aggregate variables that describe whether the epidemic has not yet reached, is currently active in, or has already passed through different regions of the spatial domain. This formulation allows the model to reproduce key qualitative features observed in aggregated incidence data, such as prolonged plateaus and multiple infection waves arising from asynchronous local outbreaks. The resulting system consists of ordinary differential equations with a relatively small number of interpretable parameters, providing a tractable framework for analytical investigation and numerical simulation. Our approach offers a parsimonious alternative for studying spatially structured epidemic dynamics when only aggregated data are available or when model simplicity is essential.