Back
Efficient numerical computation of the basic reproduction number for structured populations.
Journal article

Efficient numerical computation of the basic reproduction number for structured populations.

  • Breda D CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics - University of Udine, via delle scienze 206, 33100 Udine, Italy.
  • Florian F Institute of Mathematics-University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
  • Ripoll J Department of Computer Science, Applied Mathematics and Statistics - University of Girona, Campus Montilivi, 17003 Girona, Spain.
  • Vermiglio R CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics - University of Udine, via delle scienze 206, 33100 Udine, Italy.
  • 2020-09-02
Published in:
  • Journal of computational and applied mathematics. - 2021
47A75
47D06
65J10
65L03
65L15
65M70
65Pxx
92D25
92D30
92D40
Next generation operator
Pseudospectral collocation
Spectral approximation
Spectral radius
Stability analysis of equilibria
Structured population dynamics
English 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.
Language
  • English
Open access status
green
Identifiers
Persistent URL
https://sonar.ch/global/documents/285384
Statistics
Document views: 37 File downloads: