key: cord-289901-xb1wg3xv
authors: Krantz, Steven G.; Rao, Arni S.R. Srinivasa
title: Level of underreporting including underdiagnosis before the first peak of COVID-19 in various countries: Preliminary retrospective results based on wavelets and deterministic modeling
date: 2020-04-09
journal: Infection control and hospital epidemiology
DOI: 10.1017/ice.2020.116
sha: 
doc_id: 289901
cord_uid: xb1wg3xv

nan

New methods using harmonic analysis and wavelets that we are developing-some of them recently accepted-will be of timely use. 5 We propose a model-based evaluation of underreporting of coronavirus in various countries using the methods we recently developed using harmonic analysis, 5 that is, to develop full epidemic data from partial data (using a wavelet approach). However, the current article is a preliminary analysis and modeling was done using the data available as of March 9, 2020. These data do not represent the pandemic in its entire scale; such data will need to be reevaluated when the pandemic is completely controlled. However, our predictions for underreporting as of March 9 in a couple of European countries were close to the reported number of COVID-19 cases as more cases surfaced from March 9 to March 16, 2020. Wavelets of reported cases and adjusted estimates with the underreported cases are shown in Figure 1 . We also anticipate using other techniques [5] [6] [7] [8] [9] to further understand the reporting once more data become available.

We collected COVID-19 and population data for each country from the World Health Organization (WHO), 1 Worldometer, 2 and World Bank 10 sources. We used population densities, proportion of the population living in urban areas, and populations delineated by 3 age groups: 0-14 years, 15-64 years, and ≥65 years. Furthermore, we considered daily new cases (>10) up to the first reported peak of COVID-19 cases and the corresponding date ranges for all the countries for which such data were available. This range of days varied between 8 and 16 days (Table 1) . We use 2 coupled differential equations and the United States: 0.75 and 1.5. The difference between model-predicted numbers and the actual numbers reported within the range were treated as underreported, which includes underdiagnosed cases. We constructed the Meyer wavelets for the reported and adjusted data after adjusting the infected number in the population for underreporting. The Meyer wavelet is a differentiable function, ! ð Þ, which is infinitely differentiable in the domain with a function u as follows: Table 1 .

Here, u x ð Þ ¼ 0 for x<0, u x ð Þ ¼ x for x 2 0; 1 ð Þ, and u x ð Þ ¼ 1 for x1 For further details, please refer to Krantz et al 5 and Krantz. 9 As of March 16, 2020, we did not have enough data on COVID-19 transmissibility rates from infected to uninfected persons based on migration of populations to construct countrywide networks. We also had no clear idea of the duration that SARS-CoV-2 virus remains active on nonliving surfaces such as plastics, metals, paper, etc; thus, we did not consider the interaction between humans and nonliving surfaces. Mathematical modeling can be made more complex by adding more parameters, but caution is necessary to ensure that these studies are well designed and that these parameters use readily available, scientifically collected data. Once we obtain more data on the duration of COVID-19 living on nonliving surfaces, we can build more complex models with more parameters.

WHO situational report-49

Identification of COVID-19 can be quicker through artificial intelligence framework using a mobile phone-based survey in the populations when cities and towns are under quarantine

Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study

True epidemic growth construction through harmonic analysis

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Acknowledgments. We thank the journal's Editor-in-Chief, Associate Editor (Handling), and the Statistical Consultant for their constructive comments.Financial support. No financial support was provided relevant to this article.

Authors contributions. Both the authors contributed in writing. ASRS Rao designed the study, developed the methods, collected data, performed analysis, computing, wrote the first draft. SG Krantz designed the study, contributed in writing, performed analysis, editing the draft.