Collocation of Next-Generation Operators for Computing the Basic Reproduction Number of Structured Populations
Open Access
- 31 October 2020
- journal article
- research article
- Published by Springer Science and Business Media LLC in Journal of Scientific Computing
- Vol. 85 (2), 1-33
- https://doi.org/10.1007/s10915-020-01339-1
Abstract
We contribute a full analysis of theoretical and numerical aspects of the collocation approach recently proposed by some of the authors to compute the basic reproduction number of structured population dynamics as spectral radius of certain infinite-dimensional operators. On the one hand, we prove under mild regularity assumptions on the models coefficients that the concerned operators are compact, so that the problem can be properly recast as an eigenvalue problem thus allowing for numerical discretization. On the other hand, we prove through detailed and rigorous error and convergence analyses that the method performs the expected spectral accuracy. Several numerical tests validate the proposed analysis by highlighting diverse peculiarities of the investigated approach.Keywords
Funding Information
- Gruppo Nazionale per il Calcolo Scientifico
- Japan Society for the Promotion of Science
- Spanish Ministry of Science and Innovation
This publication has 31 references indexed in Scilit:
- OPTIMAL LATENT PERIOD IN A BACTERIOPHAGE POPULATION MODEL STRUCTURED BY INFECTION-AGEMathematical Models and Methods in Applied Sciences, 2011
- Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time HeterogeneitySIAM Journal on Applied Mathematics, 2009
- Is Gauss Quadrature Better than Clenshaw–Curtis?SIAM Review, 2008
- Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential EquationsSIAM Journal on Scientific Computing, 2005
- Barycentric Lagrange InterpolationSIAM Review, 2004
- A MATLAB differentiation matrix suiteACM Transactions on Mathematical Software, 2000
- On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populationsJournal of Mathematical Biology, 1990
- Singular Integral EquationsPublished by Springer Science and Business Media LLC ,1989
- An Introduction to the Approximation of FunctionsMathematics of Computation, 1970
- On Interpolation IAnnals of Mathematics, 1937