Survival Dynamical Systems: individual-level survival analysis from population-level epidemic models

Wasiur KhudaBukhsh (May 6, 2020)

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Motivated by the classical Susceptible-Infected-Recovered (SIR) epidemic models proposed by Kermack and Mckendrick, we consider a class of stochastic compartmental dynamical systems with a notion of partial ordering among the compartments. We call such systems uni-directional Mass Transfer Models (MTMs). We show that there is a natural way of interpreting a uni-directional MTM as a Survival Dynamical System (SDS) that is described in terms of survival functions instead of population counts. This SDS interpretation allows us to employ tools from survival analysis to address various issues with data collection and statistical inference of unidirectional MTMs. We use the SIR model as a running example to illustrate the ideas. We also discuss several possible generalizations of the method.