Analysis of virus transmission: A stochastic transition model representation of epidemiological models

The growing literature on the transmission of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered). For ease of comparison and specification testing, we introduce a common stochastic representation of the SIR-type epidemiological models. This representation is a discrete time transition model, which allows for classifying the epidemiological models with respect to the number of states (compartments) and their interpretation. Additionally, the (stochastic) transition model eliminates several limitations of the (deterministic) continuous time epidemiological models, which are pointed out in the paper. We show that when data on aggregate compartment counts are available, all discrete time SIR-type models admit a nonlinear (pseudo) state space representation and can be consistently estimated and updated from an extended Kalman filter.