New Insights into the Estimation of Reproduction Numbers during an Epidemic
In this paper, we deal with the problem of estimating the reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics><...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
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| Series: | Vaccines |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-393X/10/11/1788 |
| _version_ | 1797466301668524032 |
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| author | Giovanni Sebastiani Ilaria Spassiani |
| author_facet | Giovanni Sebastiani Ilaria Spassiani |
| author_sort | Giovanni Sebastiani |
| collection | DOAJ |
| description | In this paper, we deal with the problem of estimating the reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> during an epidemic, as it represents one of the most used indicators to study and control this phenomenon. In particular, we focus on two issues. First, to estimate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula>, we consider the use of positive test case data as an alternative to the first symptoms data, which are typically used. We both theoretically and empirically study the relationship between the two approaches. Second, we modify a method for estimating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> during an epidemic that is widely used by public institutions in several countries worldwide. Our procedure is not affected by the problems deriving from the hypothesis of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> local constancy, which is assumed in the standard approach. We illustrate the results obtained by applying the proposed methodologies to real and simulated SARS-CoV-2 datasets. In both cases, we also apply some specific methods to reduce systematic and random errors affecting the data. Our results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> during an epidemic can be estimated by using the positive test data, and that our estimator outperforms the standard estimator that makes use of the first symptoms data. It is hoped that the techniques proposed here could help in the study and control of epidemics, particularly the current SARS-CoV-2 pandemic. |
| first_indexed | 2024-03-09T18:34:57Z |
| format | Article |
| id | doaj.art-20cfcb058ce34f01b1d4fe478caa2cf5 |
| institution | Directory Open Access Journal |
| issn | 2076-393X |
| language | English |
| last_indexed | 2024-03-09T18:34:57Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Vaccines |
| spelling | doaj.art-20cfcb058ce34f01b1d4fe478caa2cf52023-11-24T07:12:45ZengMDPI AGVaccines2076-393X2022-10-011011178810.3390/vaccines10111788New Insights into the Estimation of Reproduction Numbers during an EpidemicGiovanni Sebastiani0Ilaria Spassiani1Istituto per le Applicazioni del Calcolo Mauro Picone, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Rome, ItalyIstituto Nazionale di Geofisica e Vulcanologia (INGV), Via di Vigna Murata 605, 00143 Rome, ItalyIn this paper, we deal with the problem of estimating the reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> during an epidemic, as it represents one of the most used indicators to study and control this phenomenon. In particular, we focus on two issues. First, to estimate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula>, we consider the use of positive test case data as an alternative to the first symptoms data, which are typically used. We both theoretically and empirically study the relationship between the two approaches. Second, we modify a method for estimating <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> during an epidemic that is widely used by public institutions in several countries worldwide. Our procedure is not affected by the problems deriving from the hypothesis of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> local constancy, which is assumed in the standard approach. We illustrate the results obtained by applying the proposed methodologies to real and simulated SARS-CoV-2 datasets. In both cases, we also apply some specific methods to reduce systematic and random errors affecting the data. Our results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mi>t</mi></msub></semantics></math></inline-formula> during an epidemic can be estimated by using the positive test data, and that our estimator outperforms the standard estimator that makes use of the first symptoms data. It is hoped that the techniques proposed here could help in the study and control of epidemics, particularly the current SARS-CoV-2 pandemic.https://www.mdpi.com/2076-393X/10/11/1788reproduction numberepidemic evolutionSARS-CoV-2estimation techniquesmathematical analysis |
| spellingShingle | Giovanni Sebastiani Ilaria Spassiani New Insights into the Estimation of Reproduction Numbers during an Epidemic Vaccines reproduction number epidemic evolution SARS-CoV-2 estimation techniques mathematical analysis |
| title | New Insights into the Estimation of Reproduction Numbers during an Epidemic |
| title_full | New Insights into the Estimation of Reproduction Numbers during an Epidemic |
| title_fullStr | New Insights into the Estimation of Reproduction Numbers during an Epidemic |
| title_full_unstemmed | New Insights into the Estimation of Reproduction Numbers during an Epidemic |
| title_short | New Insights into the Estimation of Reproduction Numbers during an Epidemic |
| title_sort | new insights into the estimation of reproduction numbers during an epidemic |
| topic | reproduction number epidemic evolution SARS-CoV-2 estimation techniques mathematical analysis |
| url | https://www.mdpi.com/2076-393X/10/11/1788 |
| work_keys_str_mv | AT giovannisebastiani newinsightsintotheestimationofreproductionnumbersduringanepidemic AT ilariaspassiani newinsightsintotheestimationofreproductionnumbersduringanepidemic |