LAUSR

The basic reproduction number (R0) often cannot be explicitly computed when dealing with continuously age‐structured epidemic models. In this paper, we numerically compute R0 of a PDE model for a human immunodeficiency virus (HIV) infection, defined as the spectral radius of a next‐generation operator. Since R0 cannot be analytically obtained, on the one hand, we discretize the linearized PDE model into a system of linear ODEs (Euler method), and on the other hand, we discretize the eigenvalue problem (pseudo‐spectral method). In both cases, we approximate R0 by the largest eigenvalue R0, n of a next‐generation matrix, and we show the convergence of R0, n to R0 as the discretization index n increases to infinity. Finally, we present several tests to check/compare the accuracy of both numerical methods.