A nonautonomous dynamical system applied to dengue seasonality
Seasonality due to environmental influences often affects contact between species for food or shelter as well as the spread and persistence of diseases from those vector species. Epidemic models may capture seasonality patterns in a phenomenological way by making the epidemiological parameters and...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2023-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2023(1-2)/77-158.pdf |
| _version_ | 1797821769934962688 |
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| author | Julían Alejandro Olarte García |
| author_facet | Julían Alejandro Olarte García |
| author_sort | Julían Alejandro Olarte García |
| collection | DOAJ |
| description | Seasonality due to environmental influences often affects contact between species
for food or shelter as well as the spread and persistence of diseases from those vector species. Epidemic models may capture seasonality patterns in a phenomenological way by making the epidemiological parameters and the population demographics are time-periodic. A mathematical model with these features for the dengue fever is analyzed, to such an extent that the threshold between uniform persistence and extinction of the disease is established, that is: there exists a unique positive disease-free periodic solution being globally asymptotically stable when the basic reproductive number is greater that one, but it is unstable when the basic reproductive number is less than one, in whose situation there exists at least one non-trivial positive periodic solution and dengue fever is endemic in the community. At last, numerical simulations are carried out to illustrate the theoretical results. |
| first_indexed | 2024-03-13T09:57:41Z |
| format | Article |
| id | doaj.art-6f5997fe277b4aaf8b0a3c5cbe67846f |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-03-13T09:57:41Z |
| publishDate | 2023-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-6f5997fe277b4aaf8b0a3c5cbe67846f2023-05-23T13:22:10ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502023-01-01441-277158A nonautonomous dynamical system applied to dengue seasonality Julían Alejandro Olarte García0Universidad del Quind´ıo, Facultad de Ciencias B´asicas y Tecnolog´ıas, Grupo de Modelaci´on Matem´atica en Epidemiolog´ıa, Armenia (Quind´ıo), 630002, ColombiaSeasonality due to environmental influences often affects contact between species for food or shelter as well as the spread and persistence of diseases from those vector species. Epidemic models may capture seasonality patterns in a phenomenological way by making the epidemiological parameters and the population demographics are time-periodic. A mathematical model with these features for the dengue fever is analyzed, to such an extent that the threshold between uniform persistence and extinction of the disease is established, that is: there exists a unique positive disease-free periodic solution being globally asymptotically stable when the basic reproductive number is greater that one, but it is unstable when the basic reproductive number is less than one, in whose situation there exists at least one non-trivial positive periodic solution and dengue fever is endemic in the community. At last, numerical simulations are carried out to illustrate the theoretical results.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2023(1-2)/77-158.pdfaedes aegypti and dengueseasonalityperiodic systemstabilityextinctionpersistence |
| spellingShingle | Julían Alejandro Olarte García A nonautonomous dynamical system applied to dengue seasonality Rendiconti di Matematica e delle Sue Applicazioni aedes aegypti and dengue seasonality periodic system stability extinction persistence |
| title | A nonautonomous dynamical system applied to dengue seasonality |
| title_full | A nonautonomous dynamical system applied to dengue seasonality |
| title_fullStr | A nonautonomous dynamical system applied to dengue seasonality |
| title_full_unstemmed | A nonautonomous dynamical system applied to dengue seasonality |
| title_short | A nonautonomous dynamical system applied to dengue seasonality |
| title_sort | nonautonomous dynamical system applied to dengue seasonality |
| topic | aedes aegypti and dengue seasonality periodic system stability extinction persistence |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2023(1-2)/77-158.pdf |
| work_keys_str_mv | AT julianalejandroolartegarcia anonautonomousdynamicalsystemappliedtodengueseasonality AT julianalejandroolartegarcia nonautonomousdynamicalsystemappliedtodengueseasonality |