The SEIS model, or, the contact process with a latent stage

TL;DR

This paper studies the particle system version of the SEIS epidemiological model, providing bounds, convergence results, and a limiting process analysis as the latent time varies.

Contribution

It introduces the particle system perspective for the SEIS model and establishes new bounds and convergence properties not previously analyzed.

Findings

Derived bounds on critical values for the particle system

Proved convergence of critical values for small and large latent times

Identified a limiting process as latent time becomes large

Abstract

The susceptible-exposed-infectious-susceptible (SEIS) model is well-known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The compartment model is well studied, but the corresponding particle system has so far received no attention. For the particle system model in one spatial dimension, we give upper and lower bounds on the critical values, prove convergence of critical values in the limit of small and large latent time, and identify a limiting process to which the SEIS model converges in the limit of large latent time.