Testing, tracing and isolation in compartmental models
Fig 1
Schematic of an SEIR model with diagnosis described by testing and contact-tracing.
SEIR is a compartmentalised model describing susceptible (S), exposed (E—infected but not infectious), infectious (I) and removed (R) population cohorts. Individuals move between these compartments in sequence as they become exposed, infected and infectious during disease progression until recovery. The novelty here is that each compartment comprises diagnosed and undiagnosed individuals with diagnosis leading to isolation. We assume that diagnosis happens through testing or putatively through tracing. Tracing is mediated through contact, and the intersection with CI represents contact with an infectious individual. Non-infectious individuals having been isolated through contact tracing have, in effect, been misdiagnosed. Individuals transition between compartments X and Y at rates ΔX→Y which we derive in the text.