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Open accessJournal ArticleDOI: 10.7717/PEERJ.10819

CoViD-19: an automatic, semiparametric estimation method for the population infected in Italy

04 Mar 2021-PeerJ (PeerJ)-Vol. 9
Abstract: To date, official data on the number of people infected with the SARS-CoV-2-responsible for the Covid-19-have been released by the Italian Government just on the basis of a non-representative sample of population which tested positive for the swab. However a reliable estimation of the number of infected, including asymptomatic people, turns out to be crucial in the preparation of operational schemes and to estimate the future number of people, who will require, to different extents, medical attentions. In order to overcome the current data shortcoming, this article proposes a bootstrap-driven, estimation procedure for the number of people infected with the SARS-CoV-2. This method is designed to be robust, automatic and suitable to generate estimations at regional level. Obtained results show that, while official data at March the 12th report 12.839 cases in Italy, people infected with the SARS-CoV-2 could be as high as 105.789.

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Topics: Population (54%)
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Open accessJournal ArticleDOI: 10.1016/J.CHAOS.2020.110064
Abstract: In a previous article [1] we have described the temporal evolution of the Sars-Cov-2 in Italy in the time window February 24-April 1. As we can see in [1] a generalized logistic equation captures both the peaks of the total infected and the deaths. In this article our goal is to study the missing peak, i.e. the currently infected one (or total currently positive). After the April 7, the large increase in the number of swabs meant that the logistical behavior of the infected curve no longer worked. So we decided to generalize the model, introducing new parameters. Moreover, we adopt a similar approach used in [1] (for the estimation of deaths) in order to evaluate the recoveries. In this way, introducing a simple conservation law, we define a model with 4 populations: total infected, currently positives, recoveries and deaths. Therefore, we propose an alternative method to a classical SIRD model for the evaluation of the Sars-Cov-2 epidemic. However, the method is general and thus applicable to other diseases. Finally we study the behavior of the ratio infected over swabs for Italy, Germany and USA, and we show as studying this parameter we recover the generalized Logistic model used in [1] for these three countries. We think that this trend could be useful for a future epidemic of this coronavirus.

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13 Citations


Open accessJournal ArticleDOI: 10.1016/J.CHAOS.2020.110150
Abstract: In this article we study the temporal evolution of the pandemic Sars-Cov-2 in Italy by means of dynamic population models. The time window of the available population data is between February 24, and March 25. After we upgrade the data until April 1. We perform the analysis with 4 different models and we think that the best candidate to correctly described the italian situation is a generalized Logistic equation. We use two coupled differential equations that model the evolution of the severe infected and the dead. This choice is due to the fact that in Italy the pharyngeal swabs are made only to severe infected, therefore we have no information about asymptomatic people. Moreover, an important observation is that the virus spreads between Regions with some delay. Indeed, we suggest that a different analysis, region by region, would be more sensible than one on the whole Italy. In particular the region Lombardy has a behaviour very fast compared to the other ones. We show the fit and forecast of the dead and total severe infected for Italy and five regions: Lombardy, Piedmont, Emilia-Romagna, Veneto and Tuscany. Finally we perform an analysis of the peak (intended, in our study, as the maximum of the daily total severe infected) and an estimation of how many lives have been saved by means of the LockDown.

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9 Citations


Open accessJournal ArticleDOI: 10.3390/S21072435
Livio Fenga1, Mauro Gaspari2Institutions (2)
01 Apr 2021-Sensors
Abstract: COVID-19 infections can spread silently, due to the simultaneous presence of significant numbers of both critical and asymptomatic to mild cases. While, for the former reliable data are available (in the form of number of hospitalization and/or beds in intensive care units), this is not the case of the latter. Hence, analytical tools designed to generate reliable forecast and future scenarios, should be implemented to help decision-makers to plan ahead (e.g., medical structures and equipment). Previous work of one of the authors shows that an alternative formulation of the Test Positivity Rate (TPR), i.e., the proportion of the number of persons tested positive in a given day, exhibits a strong correlation with the number of patients admitted in hospitals and intensive care units. In this paper, we investigate the lagged correlation structure between the newly defined TPR and the hospitalized people time series, exploiting a rigorous statistical model, the Seasonal Auto Regressive Moving Average (SARIMA). The rigorous analytical framework chosen, i.e., the stochastic processes theory, allowed for a reliable forecasting about 12 days ahead of those quantities. The proposed approach would also allow decision-makers to forecast the number of beds in hospitals and intensive care units needed 12 days ahead. The obtained results show that a standardized TPR index is a valuable metric to monitor the growth of the COVID-19 epidemic. The index can be computed on daily basis and it is probably one of the best forecasting tools available today for predicting hospital and intensive care units overload, being an optimal compromise between simplicity of calculation and accuracy.

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Topics: Intensive care (64%)

7 Citations


Open accessPosted Content
Abstract: The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is applied to the concrete cases of Lombardy, Italy and Sao Paulo state, Brazil, showing different aspects of the epidemics. For each case we show that we may have good fits to the data up to the present, but with very large differences in the future behavior. The reasons behind such disparate outcomes are the uncertainty on the value of a key parameter, the probability that an infected individual is fully symptomatic, and on the intensity of the social distancing measures adopted. This conclusion enforces the necessity of trying to determine the real number of infected individuals in a population, symptomatic or asymptomatic.

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Topics: Population (52%)

1 Citations


Open accessJournal ArticleDOI: 10.1142/S0129183120501120
Abstract: Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution of the infectious disease. We study a system of coupled differential equations which includes the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution is therefore compared with a macroscopic law for the population $N(t)$ coming from a single, non-linear, differential equation with no explicit reference to $A(t)$, showing the equivalence of the two methods. Indeed, $N(t)$ takes into account a more complex and detailed population dynamics which permits the evaluation of the number of asymptomatic individuals also. The model is then applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for $N(t)$ has been observed in more recent data. Then the information contained in the data analysis of $N(t)$ is reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.

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Topics: Population (55%)

1 Citations


References
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15 results found


Open accessBook
05 Aug 1993-
Abstract: Statistical models in epidemiology , Statistical models in epidemiology , کتابخانه مرکزی دانشگاه علوم پزشکی تهران

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Topics: Statistical epidemiology (75%)

1,526 Citations


Open accessBook
20 Jul 1989-
Abstract: Review of selected elementary statistics random sampling relative risk and odds ratio attributable risk adjustment of data without use of multivariate models adjustment of data without use of multivariate models follow-up studies person years comparison of numerical results for various methods of adjustment the primacy of data collection.

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Topics: Multivariate statistics (59%), Odds ratio (55%), Relative risk (55%) ... read more

1,213 Citations


Open accessJournal ArticleDOI: 10.1214/AOS/1176350057
Abstract: Let $Z_i:-\infty

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Topics: Sample variance (55%)

703 Citations


Journal ArticleDOI: 10.1093/BIOMET/86.4.948
John Barnard1, Donald B. Rubin1Institutions (1)
01 Dec 1999-Biometrika
Abstract: An appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete-data inferences into a final inference, the repeated-imputation inference (Rubin, 1987). This inference is based on a t distribution and is derived from a Bayesian paradigm under the assumption that the complete-data degrees of freedom, ν com , are infinite, but the number of imputations, m, is finite. When ν com is small and there is only a modest proportion of missing data, the calculated repeated-imputation degrees of freedom, ν m , for the t reference distribution can be much larger than ν com , which is clearly inappropriate. Following the Bayesian paradigm, we derive an adjusted degrees of freedom, ν m , with the following three properties: for fixed m and estimated fraction of missing information, ν m monotonically increases in ν com ; ν m is always less than or equal to ν com ; and ν m equals ν m when ν com is infinite. A small simulation study demonstrates the superior frequentist performance when using ν m rather than ν m .

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590 Citations


Open accessBook
01 Jan 2001-
Abstract: Preface and Acknowledgements to Second Edition Preface and Acknowledgements I: The Nature of Spatial Epidemiology 1 Definitions, Terminolgy and Data Sets 11 Map Hypotheses and Modelling Approaches 12 Definitions and Data Examples 13 Further definitions 14 Some Data Examples 2Scales of Measurement and Data Availability 21 Small Scale 22 Large Scale 23 Rate Dependence 24 DataQuality and the Ecological Fallacy 25 Edge Eects 3Geographical Representation and Mapping 31 Introduction and Definitions 32 Maps and Mapping 33 Statistical Accuracy 34 Aggregation 35 Mapping Issues related toAggregated Data 36 Conclusions 4Basic Models 41 Sampling Considerations 42 Likelihood-based and Bayesian Approaches 43 Point EventModels 44 CountModels 5Exploratory Approaches, Parametric Estimation and Inference 51 ExploratoryMethods 52 Parameter Estimation 53 Residual Diagnostics 54 Hypothesis Testing 55 Edge Eects II:Important Problems in Spatial Epidemiology 6Small Scale: Disease Clustering 61 Definition of Clusters and Clustering 62 Modelling Issues 63 Hypothesis Tests for Clustering 64 Space-Time Clustering 65 Clustering Examples 66 OtherMethods related to clustering 7Small Scale: Putative Sources of Hazard 71 Introduction 72 StudyDesign 73 Problems of Inference 74 Modelling the Hazard Exposure Risk 75 Models for Case Event Data 76 ACase Event Example 77 Models for CountData 78 ACountData Example 79 OtherDirections 8 Large Scale: Disease Mapping 81 Introduction 82 Simple Statistical Representation 83 BasicModels 84 AdvancedMethods 85 Model Variants and Extensions 86 ApproximateMethods 87 MultivariateMethods 88 Evaluation ofModel Performance 89 Hypothesis Testing in DiseaseMapping 810 Space-Time DiseaseMapping 811 Spatial Survival and longitudinal data 812 DiseaseMapping: Case Studies 9Ecological Analysis and Scale Change 91 Ecological Analysis: Introduction 92 Small-ScaleModelling Issues 93 Changes of Scale andMAUP 94 A Simple Example: Sudden Infant Death in North Carolina 95 ACase Study: Malaria and IDDM 10Infectious Disease Modelling 101 Introduction 102 GeneralModelDevelopment 103 SpatialModelDevelopment 104 Modelling Special Cases for Individual Level Data 105 Survival Analysis with spatial dependence 106 Individual level data example 107 Underascertainment and Censoring 108 Conclusions 11Large Scale: Surveillance 111 Process ControlMethodology 112 Spatio-Temporal Modelling 113 Spatio-TemporalMonitoring 114 Syndromic Surveillance 115 Multivariate-Mulitfocus Surveillance 116 Bayesian Approaches 117 Computational Considerations 118 Infectious Diseases 119 Conclusions Appendix A:Monte Carlo Testing, Parametric Bootstrap and Simulation Envelopes Appendix B:Markov ChainMonte Carlo Methods Appendix C:Algorithms and Software Appendix D: Glossary of Estimators Appendix E:Software Bibliography Index

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490 Citations