# A simplified drift-diffusion model for pandemic propagation

## TL;DR

This paper introduces a simplified, analytical drift-diffusion model for pandemic propagation based on the SIR framework, providing intuitive visualization and potential policy utility.

## Contribution

It offers a quasi-analytical solution to the SIR model, mapping pandemic dynamics onto a drift-diffusion process for better interpretability and application.

## Key findings

- Model agrees well with COVID-19 data across countries.
- Provides an intuitive visualization of epidemic evolution.
- Discusses error sources and uncertainty growth over time.

## Abstract

Predicting Pandemic evolution involves complex modeling challenges, often requiring detailed discrete mathematics executed on large volumes of epidemiological data. Differential equations have the advantage of offering smooth, well-behaved solutions that try to capture overall predictive trends and averages. We further simplify one of those equations, the SIR model, by offering quasi-analytical solutions and fitting functions that agree well with the numerics, as well as COVID-19 data across a few countries. The equations provide an elegant way to visualize the evolution, by mapping onto the dynamics of an overdamped classical particle moving in the SIR configuration space, drifting down gradient of a potential whose shape is set by the model and parameters in hand. We discuss potential sources of errors in our analysis and their growth over time, and map those uncertainties into a diffusive jitter that tends to push the particle away from its minimum. The combined physical understanding and analytical expressions offered by such an intuitive drift-diffusion model could be particularly useful in making policy decisions going forward.