Survival Dynamical Systems for the Population-level Analysis of Epidemics

TL;DR

This paper introduces Survival Dynamical Systems (SDS) as a novel framework for analyzing epidemic models, enabling the use of survival analysis tools for better statistical inference of population-level epidemic dynamics.

Contribution

It develops a new interpretation of unidirectional Mass Transfer Models as SDS, facilitating improved data analysis and inference methods for epidemic modeling.

Findings

SDS provides a natural interpretation of epidemic models in terms of survival functions.

The proposed SDS-likelihood inference method is validated numerically.

Application to SIR models demonstrates practical utility.

Abstract

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 unidirectional 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. In particular, we propose and numerically validate a statistical inference procedure based on SDS-likelihoods. We use the SIR model as a running example throughout the paper to illustrate the ideas.