Testing, tracing and isolation in compartmental models

PLoS Comput Biol. 2021 Mar 4;17(3):e1008633. doi: 10.1371/journal.pcbi.1008633. eCollection 2021 Mar.


Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Basic Reproduction Number / statistics & numerical data
  • COVID-19 / diagnosis*
  • COVID-19 / epidemiology*
  • COVID-19 / transmission
  • COVID-19 Testing / methods*
  • COVID-19 Testing / statistics & numerical data
  • Computational Biology
  • Computer Simulation
  • Contact Tracing / methods*
  • Contact Tracing / statistics & numerical data
  • Epidemics* / statistics & numerical data
  • Humans
  • Mathematical Concepts
  • Models, Biological*
  • Models, Statistical
  • Quarantine / methods*
  • Quarantine / statistics & numerical data
  • SARS-CoV-2*
  • Systems Analysis