The SEIS model, or, the contact process with a latent stage. (English) Zbl 1351.60102

Foxall, Eric

J. Appl. Probab. 53, No. 3, 783-801 (2016).

Summary: The susceptible\(\to\)exposed\(\to\)infectious\(\to\)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.

MSC:

60J25	Continuous-time Markov processes on general state spaces
92D30	Epidemiology

Keywords:

SEIS model; contact process; interacting particle system