Epidemic mitigation by statistical inference from contact tracing data

Abstract

Contact tracing is an essential tool to mitigate the impact of a pandemic, such as the COVID-19 pandemic. In order to achieve efficient and scalable contact tracing in real time, digital devices can play an important role. While a lot of attention has been paid to analyzing the privacy and ethical risks of the associated mobile applications, so far much less research has been devoted to optimizing their performance and assessing their impact on the mitigation of the epidemic. We develop Bayesian inference methods to estimate the risk that an individual is infected. This inference is based on the list of his recent contacts and their own risk levels, as well as personal information such as results of tests or presence of syndromes. We propose to use probabilistic risk estimation to optimize testing and quarantining strategies for the control of an epidemic. Our results show that in some range of epidemic spreading (typically when the manual tracing of all contacts of infected people becomes practically impossible but before the fraction of infected people reaches the scale where a lockdown becomes unavoidable), this inference of individuals at risk could be an efficient way to mitigate the epidemic. Our approaches translate into fully distributed algorithms that only require communication between individuals who have recently been in contact. Such communication may be encrypted and anonymized, and thus, it is compatible with privacy-preserving standards. We conclude that probabilistic risk estimation is capable of enhancing the performance of digital contact tracing and should be considered in the mobile applications.

Keywords: Bayesian inference; belief propagation; contact tracing; epidemic spreading.

Fig. 1.

SIR model on proximity-based random network with six contacts on average per day and $\mathrm{5,00,000}$ individuals. The epidemic parameters are the same as those used by the inference algorithms: $\lambda =0.05,\mu =0.02$. In the plot, we show the average numbers (bold lines) of infected individuals vs. time among three different realizations (thin lines) of the epidemics with 200 patients zero. The system freely evolves for the first 10 d, and then, interventions start. We consider $50\%$ of the infected individuals each day as severely symptomatic. These individuals are observed as infected 5 d after their infection. Then, 1,500 tests are performed daily according to the ranking given by the algorithms. The observed infected individuals are quarantined. The parameters used for these simulations are $\tau =5$ for both SMF and CT and $t_{\text{SMF}}=15$ for SMF. obs., observations.

Fig. 2.

Effect of the control strategy on the epidemic spreading, according to the OpenABM model, in a population of 500,000 individuals. Each infected individual can either be asymptomatic or show symptoms of various degree (mild or severe). Individuals who show severe symptoms are immediately quarantined or hospitalized when symptoms emerge. In addition, half of the mildly symptomatic individuals are assumed to self-report and self-isolate as well. No direct information is available on asymptomatic (or presymptomatic) infected individuals. The number of tests based on suggestions by the inference method is fixed, while there is no limitation on tests used for symptomatic individuals. In all panels, we show the number of infected individuals in a time window of 100 d when interventions are applied starting from day 10. The number of patients zero is set to 50. Thin lines represent the results for single instances of the epidemics, while the thick lines are the averages among the different realizations. We compare the effect of an increasing number of available medical tests per day, from $\left[\mathrm{625,5000}\right]$, performed on the individuals at highest risk as evaluated by the corresponding strategy (RG, CT, SMF, and BP). We show here four selected cases to stress the qualitative differences among the methods. Here, only tested-positive individuals, and not their cohabitants, are confined. The SMF algorithm fixes the parameters $\lambda =0.02$, $\mu =1/12$, $\tau =5$, and $t_{\text{SMF}}=10$. SI Appendix has details on the parameters used in BP. obs., observations.

Fig. 3.

Effect of test inaccuracy on the evolution of the controlled epidemics. The intervention protocol is the same as Fig. 2 when 2,500 daily observations are available, only differing in the treatment of the households. The cohabitants of the tested-positive individuals are also confined. The effects of a nonnegligible FNR of the results of the medical tests are considered, ranging from 0.09 to 0.40. Four representative regimes to underline the different behavior of the risk assessment methods are shown.

Fig. 4.

Effect of a poor AF of the mobile application on the number of infected individuals. The same intervention protocol of Fig. 2 is used here for 5,000 daily observations and the quarantine of the households. Only a fraction AF of the population, from 90 to 60%, uses the mobile application.