Background: Underreporting cases of infectious diseases poses a major challenge in the analysis of their epidemiological characteristics and dynamical aspects. Without accurate numerical estimates it is difficult to precisely quantify the proportions of severe and critical cases, as well as the mortality rate. Such estimates can be provided for instance by testing the presence of the virus. However, during an ongoing epidemic, such tests’ implementation is a daunting task. This work addresses this issue by presenting a methodology to estimate underreported infections based on approximations of the stable rates of hospitalization and death. Methods: We present a novel methodology for the stable rate estimation of hospitalization and death related to the Corona Virus Disease 2019 (COVID-19) using publicly available reports from various distinct communities. These rates are then used to estimate underreported infections on the corresponding areas by making use of reported daily hospitalizations and deaths. The impact of underreporting infections on vaccination strategies is estimated under different disease-transmission scenarios using a Susceptible-Exposed-Infective-Removed-like (SEIR) epidemiological model. Results: For the considered locations, during the period of study, the estimations suggest that the number of infected individuals could reach 30% of the population of these places, representing, in some cases, more than six times the observed numbers. These results are in close agreement with estimates from independent seroprevalence studies, thus providing a strong validation of the proposed methodology. Moreover, the presence of large numbers of underreported infections can reduce the perceived impact of vaccination strategies in reducing rates of mortality and hospitalization. Conclusions: pBy using the proposed methodology and employing a judiciously chosen data analysis implementation, we estimate COVID-19 underreporting from publicly available data. This leads to a powerful way of quantifying underreporting impact on the efficacy of vaccination strategies. As a byproduct, we evaluate the impact of underreporting in the designing of vaccination strategies.

In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regularization. We propose a discrepancy-based choice for these quantities by applying a relaxed version of Morozov's discrepancy principle. Indeed, we prove the existence of the discretization level and the regularization parameter satisfying such discrepancy. We also prove associated regularizing properties concerning the Tikhonov minimizers. We conclude by presenting some numerical examples of interest.

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number density statistics of the galaxy distribution as discussed in Ribeiro, namely, the differential density γ and the integral differential density γ*. By applying the theory advanced by Ribeiro & Stoeger, which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts dN/dz are extracted from the LF and used to calculate both γ and γ* with various cosmological distance definitions, namely, area distance, luminosity distance, galaxy area distance, and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey, and γ and γ* are calculated for two cosmological models: Einstein-de Sitter and an Ω = 0.3, Ω = 0.7 standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro, as well as showing that plots of γ and γ* against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power-law pattern for redshifts higher than 0.1. These findings support Ribeiro's theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large-scale distribution of galaxies.