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How likely is it to become infected by SARS-CoV-2 after being exposed? Almost everyone wondered about this question during the COVID-19 pandemic. Contact-tracing apps1,2 recorded measurements of proximity3 and duration between nearby smartphones. Contacts—individuals exposed to confirmed cases—were notified according to public health policies such as the 2 m, 15 min guideline4,5, despite limited evidence supporting this threshold. Here we analysed 7 million contacts notified by the National Health Service COVID-19 app6,7 in England and Wales to infer how app measurements translated to actual transmissions. Empirical metrics and statistical modelling showed a strong relation between app-computed risk scores and actual transmission probability. Longer exposures at greater distances had risk similar to that of shorter exposures at closer distances. The probability of transmission confirmed by a reported positive test increased initially linearly with duration of exposure (1.1% per hour) and continued increasing over several days. Whereas most exposures were short (median 0.7 h, interquartile range 0.4–1.6), transmissions typically resulted from exposures lasting between 1 h and several days (median 6 h, interquartile range 1.4–28). Households accounted for about 6% of contacts but 40% of transmissions. With sufficient preparation, privacy-preserving yet precise analyses of risk that would inform public health measures, based on digital contact tracing, could be performed within weeks of the emergence of a new pathogen. Digital measurements of proximity and duration of exposure by the NHS COVID-19 app show a strong relation to actual infections among 7 million contacts notified in England and Wales, with longer durations translating to increased risk of transmission. [ABSTRACT FROM AUTHOR]

When an epidemic spreads into a population, it is often impractical or impossible to continuously monitor all subjects involved. As an alternative, we propose using algorithmic solutions that can infer the state of the whole population from a limited number of measures. We analyze the capability of deep neural networks to solve this challenging task. We base our proposed architecture on Graph Convolutional Neural Networks. As such, it can reason on the effect of the underlying social network structure, which is recognized as the main component in spreading an epidemic. The proposed architecture can reconstruct the entire state with accuracy above 70%, as proven by two scenarios modeled on the CoVid-19 pandemic. The first is a generic homogeneous population, and the second is a toy model of the Boston metropolitan area. Note that no retraining of the architecture is necessary when changing the model. [ABSTRACT FROM AUTHOR]

The contact structure of a population plays an important role in transmission of infection. Many ‘structured models’ capture aspects of the contact pattern through an underlying network or a mixing matrix. An important observation in unstructured models of a disease that confers immunity is that once a fraction 1 - 1 / R 0 has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunising higher-risk individuals who play a greater role in transmission. Therefore, a limited ‘first wave’ may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we set out to investigate this more systematically. While networks offer a flexible framework to model contact patterns explicitly, they suffer from several shortcomings: (i) high-fidelity network models require a large amount of data which can be difficult to harvest, and (ii) very few, if any, theoretical contact network models offer the flexibility to tune different contact network properties within the same framework. Therefore, we opt to systematically analyse a number of well-known mean-field models. These are computationally efficient and provide good flexibility in varying contact network properties such as heterogeneity in the number contacts, clustering and household structure or differentiating between local and global contacts. In particular, we consider the question of herd immunity under several scenarios. When modelling interventions as changes in transmission rates, we confirm that in networks with significant degree heterogeneity, the first wave of the epidemic confers herd immunity with significantly fewer infections than equivalent models with less or no degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect may become much more subtle. Indeed, modifying the structure disproportionately can shield highly connected nodes from becoming infected during the first wave and therefore make the second wave more substantial. We strengthen this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. Overall, we find that results regarding (disease-induced) herd immunity levels are strongly dependent on the model, the duration of the lockdown and how the lockdown is implemented in the model. [ABSTRACT FROM AUTHOR]