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Despite the appeal of screening travellers to prevent case importation during infectious disease outbreaks, evidence shows that symptom screening is largely ineffective in delaying the geographical spread of infection. Molecular tests offer high sensitivity and specificity and can detect infections earlier than symptom screening, suggesting potential for improved outcomes. However, they were used to screen travellers for COVID-19 with mixed success. To investigate molecular screening’s role in controlling COVID-19, and to quantify the effectiveness of screening for future pathogens of concern, we developed a probabilistic model that incorporates within-host viral kinetics. We then evaluated the potential effectiveness of screening travellers for influenza A, SARS-CoV-1, SARS-CoV-2, and Ebola virus. Even under highly optimistic assumptions, we found that the inability to detect recent infections always limits the effectiveness of traveller screening. We quantify this fundamental limit by proposing an estimator for the fraction of transmission that is preventable by screening. We also demonstrate that estimates of ascertainment overestimate reductions in transmission. These results highlight the essential role that quarantine and repeated testing play in infectious disease containment. Furthermore, our findings indicate that improving screening effectiveness requires the ability to detect infection much earlier than current state-of-the-art molecular tests.
Anonymous online surveys using financial incentives are an essential tool for understanding sexual networks and risk factors including attitudes, sexual behaviors, and practices. However, these surveys are vulnerable to bots attempting to exploit the incentive. We deployed an in-person, limited audience survey via QR code at select locations in North Carolina to assess geolocation application use among men who have sex with men to characterize the role of app usage on infection risk and behavior. The survey was unexpectedly posted on a social media platform and went viral. Descriptive statistics were performed on repeat responses, free-text length, and demographic consistency. Between August 2022 and March 2023, we received 4,709 responses. Only 13 responses were recorded over a 6-month period until a sharp spike occurred: over 500 responses were recorded in a single hour and over 2,000 in a single day. Although free-text responses were often remarkably sophisticated, many multiple-choice responses were internally inconsistent. To protect data quality, all online surveys must incorporate defensive techniques such as response time validation, logic checks, and IP screening. With the rise of large language models, bot attacks with sophisticated responses to open-ended questions pose a growing threat to the integrity of research studies.
The rapid evolution of SARS-CoV-2 has led to the emergence of variants of concern (VOCs) characterized by increased transmissibility, pathogenicity, and resistance to neutralizing antibodies. Identifying these variants is essential for guiding public health efforts to control COVID-19. Although whole genome sequencing (WGS) is the gold standard for variant identification, its implementation is often limited in developing countries due to resource constraints. In Bolivia, genomic surveillance is a challenge due to its limited technological infrastructure and resources. An RT-qPCR-based strategy was designed to address these limitations and detect the mutations associated with VOCs and variants of interest (VOIs). The multiplex RT-qPCR commercial kits AllplexTM Master and Variants I (Seegene®) and the ValuPanelTM (Biosearch®) were used to target mutations such as HV69/70del, E484K, N501Y, P681H, and K417N/T. They are characteristic of the Alpha (B.1.1.7), Beta (B.1.531), Gamma (P.1), Omicron (B.1.1.529), Mu (B.1.621), and Zeta (P.2) variants. A total of 157 samples collected in Cochabamba from January to November 2021 were evaluated, identifying 44 Gamma, 2 Zeta, 20 Mu, and 10 Omicron were identified. The strategy’s effectiveness was validated against WGS data generated with Oxford NanoporeTM technology, showing a concordance rate of 0.96. This highlights the value of the RT-qPCR strategy in guiding the selection of samples for WGS, enabling broader detection of new variants that cannot be identified by RT-qPCR alone.
Poor socket fit is the leading cause of prosthetic limb discomfort. However, currently clinicians have limited objective data to support and improve socket design. Finite element analysis predictions might help improve the fit, but this requires internal and external anatomy models. While external 3D surface scans are often collected in routine clinical computer-aided design practice, detailed internal anatomy imaging (e.g., MRI or CT) is not. We present a prototype statistical shape model (SSM) describing the transtibial amputated residual limb, generated using a sparse dataset of 33 MRI and CT scans. To describe the maximal shape variance, training scans are size-normalized to their estimated intact tibia length. A mean limb is calculated and principal component analysis used to extract the principal modes of shape variation. In an illustrative use case, the model is interrogated to predict internal bone shapes given a skin surface shape. The model attributes ~52% of shape variance to amputation height and ~17% to slender-bulbous soft tissue profile. In cross-validation, left-out shapes influenced the mean by 0.14–0.88 mm root mean square error (RMSE) surface deviation (median 0.42 mm), and left-out shapes were recreated with 1.82–5.75 mm RMSE (median 3.40 mm). Linear regression between mode scores from skin-only- and full-model SSMs allowed prediction of bone shapes from the skin with 3.56–10.9 mm RMSE (median 6.66 mm). The model showed the feasibility of predicting bone shapes from surface scans, which addresses a key barrier to implementing simulation within clinical practice, and enables more representative prosthetic biomechanics research.
Limited studies on the seasonality of pharyngitis and tonsillitis suggest subtle but unexplained fluctuations in case numbers that deviate from patterns seen in other respiratory diagnoses. Data on weekly acute respiratory infection diagnoses from 2010–2022, provided by the Polish National Healthcare Fund, included a total of 360 million visits. Daily mean temperature and relative humidity were sourced from the Copernicus Climate Data Store. Seasonal pattern was estimated using the STL model, while the impact of temperature was calculated with SARIMAX. A recurring early-summer wave of an unspecified pathogen causing pharyngitis and tonsillitis was identified. The strongest pattern was observed in children under 10, though other age groups also showed somewhat elevated case numbers. The reproductive number of the pathogen is modulated by warmer temperatures; however, summer holidays and pandemic restrictions interrupt its spread. The infection wave is relatively flat, suggesting either genuinely slow spread or multiple waves of related pathogens. Symptomatic data unambiguously demonstrate existence of pathogens of quite distinct characteristics. Given its consistent year-to-year pattern, identifying these potential pathogens could enhance respective treatment, including antibiotic therapy.
The chapter is fully dedicated to the theory of large deviations. To carry out the proof of the theorem and the actual computation of various distributions of large deviations, a detailed appendix is dedicated to the saddle point theorem to compute certain fundamental integrals, recurring in the theory. Lagrange transforms stem naturally from the large deviations theory, and we discuss their properties “in-line” for non-experts.
This is a rich chapter in which we delve into the study of the (weak and strong) laws of large numbers, and of the central limit theorem. The latter is first considered for sums of independent stochastic variables whose distributions have a finite variance, and then for variables with diverging variance. Several appendices report on both basic mathematical tools and lengthy details of computation. Among the first, the rules of variable change in probability are presented, Fourier and Laplace transforms are introduced, and their role as generating functionals of moments and cumulants, and the different kinds of convergence of stochastic functions are considered and exemplified.
Analysis of experimental data with several degrees of freedom is reported, starting from the Gaussian case, from the ground of the least-squares method, whose theory is detailed at the end of the chapter, for both independent and correlated data. The multi-dimensional versions of the reweighting method for unknown distributed data and of the bootstrap and the jackknife resampling methods are presented. How the possible correlation of multivariate data affects the methods is discussed and dealt with.
The foundations of modern probability theory are briefly presented and discussed for both discrete and continuous stochastic variables. Without daring to give a rigorous mathematical construction – but citing different extremely well-written handbooks on the matter – the axiomatic theory of Kolmogorov and the concepts of joint, conditional, and marginal probability are introduced, along with the operations of union and intersection of generic random events. Eventually, Bayes’ formula is put forward with some examples. This will be at the cornerstone of statistical inference methods reported in Chapters 5 and 6.
Our last chapter is devoted to entropy. With this excuse we first present Shannon’s information theory, including the derivation of his entropy, and the enunciations and proofs of the source coding theorem and of the noisy-channel coding theorem. Then, we consider dynamical systems and the production of entropy in chaotic systems, termed Kolmogorov–Sinai entropy. For non-experts or readers who require a memory jog, we make a short recap of statistical mechanics. That is just enough to tie up some knots left untied in Chapter 4, when we developed large deviations theory for independent variables. Here we generalize to correlated variables and make one application to statistical mechanics. In particular, we find out that entropy is a large deviations function, apart from constants. We end with a lightning fast introduction to configurational entropy in disordered complex systems. Just to give a tiny glimpse of … what we do for a living!
Here we face the analysis of another kind of memoryless discrete process: branching processes, otherwise termed “chain reactions” under more physical inspiration. Before that, we carefully deepen and generalize the knowledge of the very useful tool of generating functions. This will be soon applied to the study of the dynamics of a population, predicting whether it will certainly be extinct – and how fast – or it will be self-sustaining.
In this chapter we study the first example of a correlated memoryless phenomenon: the famous “drunkard’s walk”, formally termed the random walk. We begin from a very simple case, in a homogeneous and isotropic space on a discrete hypercubic lattice. Then we add traps here and there. Eventually we make a foray into the continuous regime, with the Fokker–Planck diffusion equation (which, we see, is what physicists call a Schrödinger equation in imaginary time), and the stochastic differential Langevin equation.
Here we return to discrete Markov processes, but this time with continuous-time processes. We first consider, study, and solve specific examples such as Poisson processes, divergent birth processes, and birth-and-death processes. We derive the master equations for their probability distributions, and derive and discuss important solutions. In particular, we deepen the theory of Feller for divergent birth processes. In the end we formally study the general case of Markov processes in the stationary case, writing down the forward and the backward Kolmogorov master equations.
Analysis of experimental scalar data is tackled here. Starting from basic analysis of a large number of well-behaved data, eventually displaying Gaussian distributions, we move on to Bayesian inference and face the cases of few (or no) data, sometimes badly behaved. We first present methods to analyze data whose ideal distribution is known, and then we show methods to make predictions even when our ignorance about the data distribution is total. Eventually, various resampling methods are provided to deal with time-correlated measurements, biased estimators, anomalous data, and under- or over-estimation of statistical errors.
As we realize that random walks, chain reactions, and recurrent events are all Markov chains, i.e., correlated processes without memory, in this chapter we derive a general theory, including classification and properties of the single states and of chains. In particular, we focus on the building blocks of the theory, i.e., irreducible chains, presenting and proving a number of fundamental and useful theorems. We end up deriving the balance equation for the limit probability and the approach to the limit for long times, developing and applying the Perron–Frobenius theory for non-negative matrices and the spectral decomposition for non-Hermitian matrices. Among the applications of the theory, we underline the sorting of Web pages by search engines.