# Multi-Season Analysis Reveals the Spatial Structure of Disease Spread

## TL;DR

This study introduces a tensor-driven multi-compartment SIR model to analyze and predict the spatial and seasonal dynamics of disease spread using internet search data, revealing key transmission patterns.

## Contribution

The paper develops a novel tensor-based multi-compartment SIR model and applies it to internet data to uncover spatial structure and predict disease spread for seasonal viruses.

## Key findings

- Human movement explains 27-30% of inter-state transmission.
- Model fits RSV and WNV data with R^2 of 0.70 and 0.52.
- Disease load patterns can be predicted with minimal current season data.

## Abstract

Understanding the dynamics of infectious disease spread in a heterogeneous population is an important factor in designing control strategies. Here, we develop a novel tensor-driven multi-compartment version of the classic Susceptible-Infected-Recovered (SIR) model and apply it to Internet data to reveal information about the complex spatial structure of disease spread. The model is used to analyze state-level Google search data from the US pertaining to two viruses, Respiratory Syncytial Virus (RSV), and West Nile Virus (WNV). We fit the data with correlations of $R^2=0.70$, and $0.52$ for RSV and WNV, respectively. Although no prior assumptions on spatial structure are made, human movement patterns in the US explain 27-30\% of the estimated inter-state transmission rates. The transmission rates within states are correlated with known demographic indicators, such as population density and average age. Finally, we show that the patterns of disease load for subsequent seasons can be predicted using the model parameters estimated for previous seasons and as few as $7$ weeks of data from the current season. Our results are applicable to other countries and similar viruses, allowing the identification of disease spread parameters and prediction of disease load for seasonal viruses earlier in season.