Digital measurement of SARS-CoV-2 transmission risk from 7 million contacts.

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.

Enhancing global preparedness during an ongoing pandemic from partial and noisy data.

As the coronavirus disease 2019 spread globally, emerging variants such as B.1.1.529 quickly became dominant worldwide. Sustained community transmission favors the proliferation of mutated sub-lineages with pandemic potential, due to cross-national mobility flows, which are responsible for consecutive cases surge worldwide. We show that, in the early stages of an emerging variant, integrating data from national genomic surveillance and global human mobility with large-scale epidemic modeling allows to quantify its pandemic potential, providing quantifiable indicators for pro-active policy interventions. We validate our framework on worldwide spreading variants and gain insights about the pandemic potential of BA.5, BA.2.75, and other sub- and lineages. We combine the different sources of information in a simple estimate of the pandemic delay and show that only in combination, the pandemic potentials of the lineages are correctly assessed relative to each other. Compared to a country-level epidemic intelligence, our scalable integrated approach, that is pandemic intelligence, permits to enhance global preparedness to contrast the pandemic of respiratory pathogens such as SARS-CoV-2.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models.

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Dynamic survival analysis for non-Markovian epidemic models.

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method's versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.

Estimating the state of epidemics spreading with graph neural networks.

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.

The Impact of Contact Structure and Mixing on Control Measures and Disease-Induced Herd Immunity in Epidemic Models: A Mean-Field Model Perspective.

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 [Formula: see text] 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.

Optimal timing of one-shot interventions for epidemic control.

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.

Covid-19 and Flattening the Curve: A Feedback Control Perspective.

Many of the policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution. This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution of this letter is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno - a small city in Northern Italy that has been among the most harshly hit by the pandemic.

Stereolithography in oral implantology: a comparison of surgical guides.

This article presents the use of stereolithography in oral implantology. Stereolithography is a new technology that can produce physical models by selectively solidifying an ultraviolet-sensitive liquid resin using a laser beam, reproducing the true maxillary and mandibular anatomic dimensions. With these models, it is possible to fabricate surgical guides that can place the implants in vivo in the same places and same directions as those in the planned computer simulation. A 70-year-old woman, in good health, with severe mandibular bone atrophy was rehabilitated with an over-denture supported by 2 Branemark implants. Two different surgical planning methods were considered: 1) the construction of a surgical guide evaluating clinical aspects, and 2) the surgical guide produced by stereolithographic study. The accuracy of surgical planning can reduce the problems related to bone density and dimensions. Furthermore, the stereolithographic study assured the clinicians of a superior location of fixtures in bone. Surgical planning based on stereolithographic technique is a safe procedure and has many advantages. This technologic advance has biologic and therapeutic benefits because it simplifies anatomic surgical management for improved implant placement.