Epidemic models

Alex Reinhart – Updated July 20, 2016 notebooks · refsmmat.com

Written from the perspective of someone trying to do spatiotemporal crime modeling, not disease models.

Typical epidemic models focus on individuals, not locations – they look at patients, model them as Susceptible, Infected, or Recovered, and model how people transition between states. This is the SIR model, and sets up differential equations describing transitions. Natural extensions are things like network models for the interactions between individuals, so the structure of contacts between infected and susceptible people is captured.

Metapopulation models do analyze space, but only by breaking the population into sub-populations which have connectivity dependent on spatial factors. We could, for example, have sub-populations for different neighborhoods and adjust their connectivity based on how difficult it is to get from one to the next. But that doesn’t directly model risk in space – we’re still looking at the people, not the locations. The quantity of interest for all of these models is the number of infected people as a function of time, not the spatial risk of future infections.

An overview: Lawson, A. B. (2006). Statistical Methods in Spatial Epidemiology (2nd ed.). Wiley. doi:10.1002/9780470035771

Conditional intensity model