| Autor: |
Rafael Bravo de la Parra, Luis Sanz-Lorenzo |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-24 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
1687-1847 |
| DOI: |
10.1186/s13662-021-03633-0 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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