Stochastic epidemic models and their link with methods from survival analysis

Compartmental models based on ordinary differential equations (ODE’s) quantifying the interactions between susceptible, infectious, and recovered individuals within a population have played an important role in infectious disease modeling. The aim of the present paper is to explain the link between stochastic epidemic models based on the susceptible-infectious-recovered (SIR) model, and methods from survival analysis. We illustrate how standard software for survival analysis in the statistical language R can be used to estimate pivotal parameters in the stochastic SIR model in the very much idealized situation where the epidemic is completely observed. Extensions incorporating interventions, age structure and heterogeneity are explored and illustrated.