On the basic reproduction number in continuously structured populations
In the framework of population dynamics, the basic reproduction number ℛ0 is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments, it is calculated as the spectral radius of the so‐called next‐generation operator. In...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10256/19135 |
| Online Access: | http://hdl.handle.net/10256/19135 |
| Access Level: | Open access |
| Keyword: | Operadors diferencials Teoria espectral (Matemàtica) Differential operators Spectral theory (Mathematics) |
| Summary: | In the framework of population dynamics, the basic reproduction number ℛ0 is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments, it is calculated as the spectral radius of the so‐called next‐generation operator. In continuously structured populations defined in a Banach lattice X with concentrated states at birth, one cannot define the next‐generation operator in X. In the present paper, we present an approach to compute the basic reproduction number of such models as the limit of the basic reproduction number of a sequence of models for which ℛ0 can be computed as the spectral radius of the next‐generation operator. We apply these results to some examples: the (classical) size‐dependent model, a size‐structured cell population model, a size‐structured model with diffusion in structure space (under some particular assumptions), and a (physiological) age‐structured model with diffusion in structure space. |
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