Discrete epidemic models with two time scales
Abstract The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, chang...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03633-0 |
| _version_ | 1818732183268884480 |
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| author | Rafael Bravo de la Parra Luis Sanz-Lorenzo |
| author_facet | Rafael Bravo de la Parra Luis Sanz-Lorenzo |
| author_sort | Rafael Bravo de la Parra |
| collection | DOAJ |
| description | Abstract The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities or behaviors, or others. To include a sufficiently general disease model, we first build up from first principles a discrete-time susceptible–exposed–infectious–recovered–susceptible (SEIRS) model and characterize the eradication or endemicity of the disease with the help of its basic reproduction number R 0 $\mathcal{R}_{0}$ . Then, we propose a general full model that includes sequentially the two processes at different time scales and proceed to its analysis through a reduced model. The basic reproduction number R ‾ 0 $\overline{\mathcal{R}}_{0}$ of the reduced system gives a good approximation of R 0 $\mathcal{R}_{0}$ of the full model since it serves at analyzing its asymptotic behavior. As an illustration of the proposed general framework, it is shown that there exist conditions under which a locally endemic disease, considering isolated patches in a metapopulation, can be eradicated globally by establishing the appropriate movements between patches. |
| first_indexed | 2024-12-17T23:29:31Z |
| format | Article |
| id | doaj.art-406dc9ddfadf4f9ca1bc31c8fdfec4bd |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-17T23:29:31Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-406dc9ddfadf4f9ca1bc31c8fdfec4bd2022-12-21T21:28:41ZengSpringerOpenAdvances in Difference Equations1687-18472021-10-012021112410.1186/s13662-021-03633-0Discrete epidemic models with two time scalesRafael Bravo de la Parra0Luis Sanz-Lorenzo1U.D. Matemáticas, Universidad de AlcaláDpto. Matemática Aplicada, ETSI Industriales, Universidad Politécnica de MadridAbstract The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities or behaviors, or others. To include a sufficiently general disease model, we first build up from first principles a discrete-time susceptible–exposed–infectious–recovered–susceptible (SEIRS) model and characterize the eradication or endemicity of the disease with the help of its basic reproduction number R 0 $\mathcal{R}_{0}$ . Then, we propose a general full model that includes sequentially the two processes at different time scales and proceed to its analysis through a reduced model. The basic reproduction number R ‾ 0 $\overline{\mathcal{R}}_{0}$ of the reduced system gives a good approximation of R 0 $\mathcal{R}_{0}$ of the full model since it serves at analyzing its asymptotic behavior. As an illustration of the proposed general framework, it is shown that there exist conditions under which a locally endemic disease, considering isolated patches in a metapopulation, can be eradicated globally by establishing the appropriate movements between patches.https://doi.org/10.1186/s13662-021-03633-0Discrete-time epidemic modelTime scalesDisease eradication or persistence |
| spellingShingle | Rafael Bravo de la Parra Luis Sanz-Lorenzo Discrete epidemic models with two time scales Advances in Difference Equations Discrete-time epidemic model Time scales Disease eradication or persistence |
| title | Discrete epidemic models with two time scales |
| title_full | Discrete epidemic models with two time scales |
| title_fullStr | Discrete epidemic models with two time scales |
| title_full_unstemmed | Discrete epidemic models with two time scales |
| title_short | Discrete epidemic models with two time scales |
| title_sort | discrete epidemic models with two time scales |
| topic | Discrete-time epidemic model Time scales Disease eradication or persistence |
| url | https://doi.org/10.1186/s13662-021-03633-0 |
| work_keys_str_mv | AT rafaelbravodelaparra discreteepidemicmodelswithtwotimescales AT luissanzlorenzo discreteepidemicmodelswithtwotimescales |