Tracking the emergence of disparities in the subnational spread of COVID-19 in Brazil using an online application for real-time data visualisation: A longitudinal analysis

Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks; an application to COVID-19

We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases. We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing. The model is fitted to data reported for the early spread of COVID-19 in South Korea, Brazil, and Venezuela. The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries. Using the fitted values, we estimate the effective reproduction number R e and investigate its responses to varied control scenarios of contact tracing. Alongside the positivity of solutions, and a stability analysis of the disease-free equilibrium are provided.

Multilevel Coarsening for Interactive Visualization of Large Bipartite Networks

Bipartite networks are pervasive in modeling real-world phenomena and play a fundamental role in graph theory. Interactive exploratory visualization of such networks is an important problem, and particularly challenging when handling large networks. In this paper we present results from an investigation on using a general multilevel method for this purpose. Multilevel methods on networks have been introduced as a general approach to increase scalability of community detection and other complex optimization algorithms. They employ graph coarsening algorithms to create a hierarchy of increasingly coarser (reduced) approximations of an original network. Multilevel coarsening has been applied, e.g., to the problem of drawing simple (“unipartite”) networks. We build on previous work that extended multilevel coarsening to bipartite graphs to propose a visualization interface that uses multilevel coarsening to compute a multi-resolution hierarchical representation of an input bipartite network. From this hierarchy, interactive node-link drawings are displayed following a genuine route of the “overview first, zoom and filter, details on demand” visual information seeking mantra. Analysts may depart from the coarsest representation and select nodes or sub-graphs to be expanded and shown at greater detail. Besides intuitive navigation of large-scale networks, this solution affords great flexibility, as users are free to select different coarsening strategies in different scenarios. We illustrate its potential with case studies involving real networks on distinct domains. The experimental analysis shows our strategy is effective to reveal topological structures, such as communities and holes, that may remain hidden in a conventional node-link layout. It is also useful to highlight connectivity patterns across the bipartite layers, as illustrated in an example that emphasizes the correlation between diseases and genes in genetic disorders, and in a study of a scientific collaboration network of authors and papers.

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

Simple Summary

In the past two years, the COVID-19 incidence curves and reproduction number Rt have been the main metrics used by policy makers and journalists to monitor the spread of this global pandemic. However, these metrics are not always reliable in the short term, because of a combination of delay in detection, administrative delays and random noise. In this article, we present a complete model of COVID-19 incidence, faithfully reconstructing the incidence curve and reproduction number from the renewal equation of the disease and precisely estimating the biases associated with periodic weekly bias, festive day bias and residual noise.

Abstract

The sanitary crisis of the past two years has focused the public’s attention on quantitative indicators of the spread of the COVID-19 pandemic. The daily reproduction number Rt, defined by the average number of new infections caused by a single infected individual at time t, is one of the best metrics for estimating the epidemic trend. In this paper, we provide a complete observation model for sampled epidemiological incidence signals obtained through periodic administrative measurements. The model is governed by the classic renewal equation using an empirical reproduction kernel, and subject to two perturbations: a time-varying gain with a weekly period and a white observation noise. We estimate this noise model and its parameters by extending a variational inversion of the model recovering its main driving variable Rt. Using Rt, a restored incidence curve, corrected of the weekly and festive day bias, can be deduced through the renewal equation. We verify experimentally on many countries that, once the weekly and festive days bias have been corrected, the difference between the incidence curve and its expected value is well approximated by an exponential distributed white noise multiplied by a power of the magnitude of the restored incidence curve.