Efficient numerical computation of the basic reproduction number for structured population
| Autor: | Jordi Ripoll, Rossana Vermiglio, Francesco Florian, Dimitri Breda |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematical optimization
next generation operator Spectral radius Computation G.1 Population 65L03 65Pxx Dynamical Systems (math.DS) 92D25 structured population dynamics stability analysis of equilibria next generation operator spectral radius spectral approximation pseudospectral collocation Article stability analysis of equilibria 92D30 Convergence (routing) FOS: Mathematics Quantitative Biology::Populations and Evolution 47D06 Mathematics - Numerical Analysis Mathematics - Dynamical Systems education 65M70 Eigenvalues and eigenvectors Mathematics spectral radius 65J10 Smoothness education.field_of_study Collocation Applied Mathematics 65L15 65Pxx 65L03 65L15 65M70 65J10 92D25 92D30 92D40 47D06 47A75 pseudospectral collocation Numerical Analysis (math.NA) structured population dynamics Computational Mathematics spectral approximation 92D40 47A75 Basic reproduction number |
| Zdroj: | Journal of Computational and Applied Mathematics |
| Popis: | As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next generation operators is rather elegant, but simultaneously poses serious obstacles to its practical determination. In this work we address the problem numerically by reducing the relevant operators to matrices through a pseudospectral collocation, eventually computing the sought quantity by solving finite-dimensional eigenvalue problems. The approach is illustrated for two classes of models, respectively from ecology and epidemiology. Several numerical tests demonstrate experimentally important features of the method, like fast convergence and influence of the smoothness of the models' coefficients. Examples of robust analysis of instances of specific models are also presented to show potentialities and ease of application. Comment: 25 pages; 10 figures, submitted for publication |
| Databáze: | OpenAIRE |
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