Parameter estimation for contact tracing in graph-based models.

We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to determine the degree distribution of the random tree as well as the tracing probability. Since we do not discover all infectees via contact tracing, this estimation is non-trivial. To keep things simple and stable, we develop an approximation suited for realistic situations (contract tracing probability small, or the probability for the detection of index cases small). In this approximation, the only epidemiological parameter entering the estimator is R0. The estimator is tested in a simulation study and is furthermore applied to COVID-19 contact tracing data from India. The simulation study underlines the efficiency of the method. For the empirical COVID-19 data, we compare different degree distributions and perform a sensitivity analysis. We find that particularly a power-law and a negative binomial degree distribution fit the data well and that the tracing probability is rather large. The sensitivity analysis shows no strong dependency of the estimates on the reproduction number. Finally, we discuss the relevance of our findings.

The impact of digital contact tracing on the SARS-CoV-2 pandemic-a comprehensive modelling study.

Contact tracing is one of several strategies employed in many countries to curb the spread of SARS-CoV-2. Digital contact tracing (DCT) uses tools such as cell-phone applications to improve tracing speed and reach. We model the impact of DCT on the spread of the virus for a large epidemiological parameter space consistent with current literature on SARS-CoV-2. We also model DCT in combination with random testing (RT) and social distancing (SD). Modelling is done with two independently developed individual-based (stochastic) models that use the Monte Carlo technique, benchmarked against each other and against two types of deterministic models. For current best estimates of the number of asymptomatic SARS-CoV-2 carriers (approximately 40%), their contagiousness (similar to that of symptomatic carriers), the reproductive number before interventions ( R 0 at least 3) we find that DCT must be combined with other interventions such as SD and/or RT to push the reproductive number below one. At least 60% of the population would have to use the DCT system for its effect to become significant. On its own, DCT cannot bring the reproductive number below 1 unless nearly the entire population uses the DCT system and follows quarantining and testing protocols strictly. For lower uptake of the DCT system, DCT still reduces the number of people that become infected. When DCT is deployed in a population with an ongoing outbreak where O (0.1%) of the population have already been infected, the gains of the DCT intervention come at the cost of requiring up to 15% of the population to be quarantined (in response to being traced) on average each day for the duration of the epidemic, even when there is sufficient testing capability to test every traced person.

Exact and approximate formulas for contact tracing on random trees.

We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously mixing populations to trees. Based on these formulas, we discuss the influence of randomness in the tree and the basic reproduction number. We find the well known results for the homogeneously mixing case as a limit of the present model (tree-shaped contact graph). Furthermore, we develop approximate mean field equations for the dynamics on trees, and - using the message passing method - also for the configuration model. The interpretation and implications of the results are discussed.