One of the most common ways to model the spread of an infectious disease in a population is through compartment models, so called because they divide the population into compartments, with each person residing in one compartment. Perhaps the most common variant is the Susceptible-Infected-Recovered (SIR) model, where people are in one of those 3 compartments. A simple set of 3 differential equations describes the movement of people between these compartments. Thus, for example, the number of infected people in the next time step is dependent on the number of currently susceptible individuals, the number of infected people they come into contact with, and the infection rate, minus the number of people who recover in a time step.
However, in most cases people don’t just belong to one compartment, because populations are not homogenous. For example, it makes sense to divide the population not just to the SIR compartments but also according to the country they live in.
Today we publish an extended SIR model which can model homogeneous populations, divided, for example, by area of residence, age group, etc. By fitting the model to Google Trends data for two common viruses, we reveal information about the complex spatial structure of disease spread.
The viruses we rested were Respiratory Syncytial Virus (RSV) and West Nile Virus (WNV). No COVID-19 data here. Sorry.
Although we make no prior assumptions on spatial structure, 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.
Our model also allows prediction of disease spread in subsequent seasons using the model parameters estimated for previous seasons and as few as 7 weeks of data from the current season.
The work was done mostly by our then intern, Dr. Inbar Seroussi.