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Collocation of next-generation operators for computing the basic reproduction number of structured populations. (English) Zbl 07273331
Summary: 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.
##### MSC:
 65J10 Numerical solutions to equations with linear operators (do not use 65Fxx) 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 37N25 Dynamical systems in biology 47A75 Eigenvalue problems for linear operators
##### Software:
Differentiation Matrix Suite; Matlab
Full Text:
##### References:
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