A stochastic epidemic model with two quarantine states and limited carrying capacity for quarantine

We study extreme values in an SIQS (susceptible. infectious. quarantined. susceptible) model with two different states for quarantine, termed quarantined susceptible and quarantined infective, and limited carrying capacity for the quarantine compartment. The aim is to characterize the probability distribution of various stochastic descriptors, such as the random length of an outbreak, the time until the quarantine compartment is full for the first time, the maximum number of simultaneously quarantined individuals, and the maximum number of simultaneously infected individuals during an outbreak. For illustrative purposes, a numerical study of the model is performed to show the influence of certain key parameters on the spread of a disease amongst a homogeneously mixing community of individuals. (C) 2019 Elsevier B.V. All rights reserved.