Collocation of next-generation operators for computing the basic reproduction number of structured populations

DOI10.1007/s10915-020-01339-1zbMath1453.92006OpenAlexW3095381560WikidataQ101456185 ScholiaQ101456185MaRDI QIDQ2211085

Toshikazu Kuniya, Jordi Ripoll, Rossana Vermiglio, Dimitri Breda

Publication date: 12 November 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-020-01339-1

zbMATH Keywords

spectral radiusbasic reproduction numberspectral approximationstructured population dynamicspseudospectral collocationnext-generation operatorstability analysis of equilibria

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Population dynamics (general) (92D25) Eigenvalue problems for linear operators (47A75) Numerical solutions to equations with linear operators (65J10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Computational methods for problems pertaining to biology (92-08)

Related Items

Bivariate collocation for computing \(R_0\) in epidemic models with two structures, Data assimilation predictive GAN (DA-PredGAN) applied to a spatio-temporal compartmental model in epidemiology, A convergent numerical scheme to a McKendrick–von Foerster equation with diffusion, A Numerical Method for the Stability Analysis of Linear Age-Structured Models with Nonlocal Diffusion, A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition, Efficient numerical computation of the basic reproduction number for structured populations, Numerical threshold of linearly implicit Euler method for nonlinear infection-age SIR models, Global stability analysis of a delay cell-population model of hepatitis B infection with humoral immune response

Uses Software

• Matlab
• Differentiation Matrix Suite

Cites Work

• On a new perspective of the basic reproduction number in heterogeneous environments
• On the definition and the computation of the basic reproduction ratio \(R_ 0\) in models for infectious diseases in heterogeneous populations
• Functional analysis, Sobolev spaces and partial differential equations
• On the reproduction number of a gut microbiota model
• The asymptotic behaviour of semigroups of linear operators
• A theta-scheme approximation of basic reproduction number for an age-structured epidemic system in a finite horizon
• Efficient numerical computation of the basic reproduction number for structured populations
• The basic reproduction number \(R_0\) in time-heterogeneous environments
• Numerical approximation of the basic reproduction number for a class of age-structured epidemic models
• On interpolation. I. Quadrature- and mean-convergence in the Lagrange- interpolation
• OPTIMAL LATENT PERIOD IN A BACTERIOPHAGE POPULATION MODEL STRUCTURED BY INFECTION-AGE
• Stability of Linear Delay Differential Equations
• PC-Based Sensitivity Analysis of the Basic Reproduction Number of Population and Epidemic Models
• The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results
• Interpolation Processes
• Spectral Methods in MATLAB
• A practical approach to R₀ in continuous‐time ecological models
• Barycentric Lagrange Interpolation
• On the basic reproduction number in continuously structured populations
• Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity
• Age-Structured Population Dynamics in Demography and Epidemiology
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
• Linear integral equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item