Bivariate collocation for computing R0 in epidemic models with two structures

Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the “spatial” variables represent individual traits, called structures. For with two structures, we propose a numerical technique to approximate R0, which measures transmissibility of an infectious disease and, rigorously, is defined dominant eigenvalue next generation operator. Via bivariate collocation and cubature on tensor grids, latter approximated finite-dimensional matrix, so that its easily computed standard techniques. We use test examples investigate experimentally behavior approximation: convergence order appears infinite when corresponding eigenfunction smooth, finite for less regular eigenfunctions. To demonstrate effectiveness more realistic applications, present new model structured by demographic age immunity, study approximation R0 in some particular cases interest.