Approximating reproduction numbers: a general numerical method for age-structured models
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914721394851840 |
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| author | De Reggi, Simone Scarabel, Francesca Vermiglio, Rossana |
| author_facet | De Reggi, Simone Scarabel, Francesca Vermiglio, Rossana |
| contents | In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_13477 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Approximating reproduction numbers: a general numerical method for age-structured models De Reggi, Simone Scarabel, Francesca Vermiglio, Rossana Populations and Evolution Numerical Analysis Dynamical Systems 34L16, 37N25, 65L15, 65L60, 65P99, 92D25, 92D30 In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases. |
| title | Approximating reproduction numbers: a general numerical method for age-structured models |
| topic | Populations and Evolution Numerical Analysis Dynamical Systems 34L16, 37N25, 65L15, 65L60, 65P99, 92D25, 92D30 |
| url | https://arxiv.org/abs/2312.13477 |