On the Estimation of the Time-Dependent Transmission Rate in Epidemiological Models
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913628654927872 |
|---|---|
| author | Zubelli, Jorge P. Loria, Jennifer Albani, Vinicius V. L. |
| author_facet | Zubelli, Jorge P. Loria, Jennifer Albani, Vinicius V. L. |
| contents | The COVID-19 pandemic highlighted the need to improve the modeling, estimation, and prediction of how infectious diseases spread. SEIR-like models have been particularly successful in providing accurate short-term predictions. This study fills a notable literature gap by exploring the following question: Is it possible to incorporate a nonparametric susceptible-exposed-infected-removed (SEIR) COVID-19 model into the inverse-problem regularization framework when the transmission coefficient varies over time? Our positive response considers varying degrees of disease severity, vaccination, and other time-dependent parameters. In addition, we demonstrate the continuity, differentiability, and injectivity of the operator that link the transmission parameter to the observed infection numbers. By employing Tikhonov-type regularization to the corresponding inverse problem, we establish the existence and stability of regularized solutions. Numerical examples using both synthetic and real data illustrate the model's estimation accuracy and its ability to fit the data effectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Estimation of the Time-Dependent Transmission Rate in Epidemiological Models Zubelli, Jorge P. Loria, Jennifer Albani, Vinicius V. L. Populations and Evolution Numerical Analysis 34A55, 92D30, 65L08 The COVID-19 pandemic highlighted the need to improve the modeling, estimation, and prediction of how infectious diseases spread. SEIR-like models have been particularly successful in providing accurate short-term predictions. This study fills a notable literature gap by exploring the following question: Is it possible to incorporate a nonparametric susceptible-exposed-infected-removed (SEIR) COVID-19 model into the inverse-problem regularization framework when the transmission coefficient varies over time? Our positive response considers varying degrees of disease severity, vaccination, and other time-dependent parameters. In addition, we demonstrate the continuity, differentiability, and injectivity of the operator that link the transmission parameter to the observed infection numbers. By employing Tikhonov-type regularization to the corresponding inverse problem, we establish the existence and stability of regularized solutions. Numerical examples using both synthetic and real data illustrate the model's estimation accuracy and its ability to fit the data effectively. |
| title | On the Estimation of the Time-Dependent Transmission Rate in Epidemiological Models |
| topic | Populations and Evolution Numerical Analysis 34A55, 92D30, 65L08 |
| url | https://arxiv.org/abs/2412.19930 |