Numerical approximation of basic reproduction number for an age‐structured HIV infection model with both virus‐to‐cell and cell‐to‐cell transmissions

Abstract

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.