  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.
