# A Multi-Region SEIR Model Incorporating Inter-County Mobility and Time-Dependent Transmission Dynamics: Application to COVID-19 Disease Outbreak Data in North Carolina

## TL;DR

This paper introduces a spatially detailed SEIR model for tracking and predicting the spread of diseases like COVID-19, using mobility and population data across North Carolina counties.

## Contribution

The novelty lies in integrating inter-county mobility and time-dependent transmission rates into a multi-region SEIR model calibrated with real-world data.

## Key findings

- The model achieved the lowest error when combining county- and state-level least squares with a quadratic transmission rate polynomial.
- Simulations showed how mobility patterns and transmission rate changes in one county can affect neighboring regions.
- Population density was found to correlate with transmission dynamics, reducing the number of required parameters.

## Abstract

Classical infectious disease compartmental models typically do not incorporate spatial heterogeneity or mobility. We develop a multi-region susceptible-exposed-infected-recovered (SEIR) model in which disease dynamics are coupled via inter-region mobility and the transmission rate is both region and time dependent. We calibrate the model using rolling averages of daily COVID-19 data in all 100 North Carolina counties. Mobility parameters are prescribed using daily inter-county commuter data. The number of transmission rate parameters is substantially reduced by hypothesizing that the dynamics correlate with county-level population density. Parameter estimation is carried out using several objective functions with error terms at different scales. An additive combination of least squares error at the county-level and the state-level, along with a quadratic transmission rate polynomial, yields the lowest overall error at both spatial scales. The calibrated model is used to simulate regional effects of perturbing disease transmission rates in adjacent counties and to illustrate effects of the state’s mobility infrastructure on disease dynamics and spread for a new disease outbreak.