Testing, tracing and isolation in compartmental models

Abstract

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 computationally efficiency is such that it 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.

Determining the level of social distancing necessary to avoid a second COVID-19 epidemic wave: a modelling study for North East London 

“…Our results suggest that lockdown is a highly effective strategy in reducing infections and mortality, and that lifting of lockdown fully in the near term would likely lead to a resurgence of cases and a secondary COVID-19 peak, as shown by other modelling studies [13][14][15][16][17].…”

“…Since the onset of the epidemic in the UK, mathematical modelling has been widely used to understand the spread of COVID-19 across different settings [12], and to design optimal strategies to reduce future burden and prevent a second wave. Different mathematical models have been utilised: deterministic models on whole populations and rooted in using equations tracking Susceptible-Exposed-Infectious-Removed (SEIR) populations [13], sometimes age-strati ed [14,15]; and stochastic i.e. individual-based models [16,17] for transmission between individuals in a population.…”

Modelling the health and economic impacts of different testing and tracing strategies for COVID-19 in the UK

“…A non-infectious individual that is "diagnosed" has effectively been misdiagnosed and the result is that they are needlessly required to isolate. Individuals transition between compartments X and Y at rates ∆ X→Y which we derive in Sturniolo et al 24 from which this figure is reproduced.…”

“…The model is available from GitHub and is archived with Zenodo 40 . The impact analysis was conducted using the SEIR-TTI compartmental model shown schematically in Figure 2 and with details provided in Sturniolo et al 24 The model is an extended version of the classic SEIR model that incorporates probabilistically the effects of testing, contact tracing, and isolation 24 .…”

“…In this study, we handle these limitations by directing our focus on understanding the most important features of the combined model. We use a Susceptible-Exposed-Infectious-Removed (SEIR) model 24 and a simplified economic analysis to explore the pattern of infections and deaths from COVID-19 and the economic impact of different NPIs in the UK. To make a wide range of scenarios accessible, we provide a user-friendly web interface that allows policymakers to explore trade-offs between different scenarios.…”