Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic
Background: The age of infection plays an important role in assessing an individual’s daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Biology |
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| Online Access: | https://www.mdpi.com/2079-7737/11/12/1825 |
| _version_ | 1797461332553891840 |
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| author | Jacques Demongeot Pierre Magal |
| author_facet | Jacques Demongeot Pierre Magal |
| author_sort | Jacques Demongeot |
| collection | DOAJ |
| description | Background: The age of infection plays an important role in assessing an individual’s daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article’s main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model. Results: We present some results of the parameters’ identification of the model when all the eigenvalues are known. This method was applied to Japan’s third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month. Conclusion: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data. |
| first_indexed | 2024-03-09T17:17:56Z |
| format | Article |
| id | doaj.art-1ef07176dafa4081af9687e5d0e666a3 |
| institution | Directory Open Access Journal |
| issn | 2079-7737 |
| language | English |
| last_indexed | 2024-03-09T17:17:56Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Biology |
| spelling | doaj.art-1ef07176dafa4081af9687e5d0e666a32023-11-24T13:24:09ZengMDPI AGBiology2079-77372022-12-011112182510.3390/biology11121825Spectral Method in Epidemic Time Series: Application to COVID-19 PandemicJacques Demongeot0Pierre Magal1Université Grenoble Alpes, AGEIS EA7407, F-38700 La Tronche, FranceUniversité Bordeaux, IMB, UMR 5251, F-33400 Talence, FranceBackground: The age of infection plays an important role in assessing an individual’s daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article’s main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model. Results: We present some results of the parameters’ identification of the model when all the eigenvalues are known. This method was applied to Japan’s third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month. Conclusion: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.https://www.mdpi.com/2079-7737/11/12/1825epidemic modelstime seriesspectral methodspectral truncation methodphenomenological models |
| spellingShingle | Jacques Demongeot Pierre Magal Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic Biology epidemic models time series spectral method spectral truncation method phenomenological models |
| title | Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic |
| title_full | Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic |
| title_fullStr | Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic |
| title_full_unstemmed | Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic |
| title_short | Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic |
| title_sort | spectral method in epidemic time series application to covid 19 pandemic |
| topic | epidemic models time series spectral method spectral truncation method phenomenological models |
| url | https://www.mdpi.com/2079-7737/11/12/1825 |
| work_keys_str_mv | AT jacquesdemongeot spectralmethodinepidemictimeseriesapplicationtocovid19pandemic AT pierremagal spectralmethodinepidemictimeseriesapplicationtocovid19pandemic |