SIRSEIR

SIRSEIR is a class of compartmental models in epidemiology that extends the traditional SIR framework by incorporating latent or exposed stages typical of SEIR models, while retaining elements of direct infection found in SIR models. The aim is to capture diseases that can spread both through immediate infectious contact and through a latent period before infectiousness, providing a flexible tool for studying outbreak dynamics and intervention strategies.

In common realizations, the population is divided into core compartments: Susceptible (S), Exposed (E) for individuals in a latent period, Infectious (I) for those capable of transmitting, and Recovered/Removed (R). Some variants include subcategories of infectious states, such as presymptomatic or symptomatic, to reflect differing levels of infectiousness or detection. Transitions typically follow a path from S to E or I upon exposure, E to I as the latent period ends, and I to R as individuals recover or are removed from transmission.

Dynamics in SIRSEIR are governed by transmission and progression parameters that control how quickly people move between states. A basic reproduction number, R0, emerges from these parameters and helps assess the potential for spread. The model’s dual structure enables exploration of interventions targeting both latent progression (e.g., reducing exposure) and infectiousness (e.g., isolation or treatment).

Applications and limitations: SIRSEIR is used for outbreak forecasting, scenario analysis, and policy planning, particularly for diseases with significant latent periods and pre-symptomatic or asymptomatic transmission. It requires data to estimate parameters, and identifiability can be challenging due to reporting biases and undiscovered latent cases. History of the term reflects a generalization of SIR and SEIR concepts, with various formulations offered in the literature.