Numerical approximation of the basic reproduction number for a class of age-structured epidemic models

We are concerned with the numerical approximation of the basic reproduction number R0, which is the well-known epidemiological threshold value defined by the spectral radius of the next generation operator. For a class of age-structured epidemic models in infinite-dimensional spaces, R0 has the abstract form and cannot be explicitly calculated in general. We discretize the linearized equation for the infective population into a system of ordinary differential equations in a finite n-dimensional space and obtain a corresponding threshold value R0,n, which can be explicitly calculated as the positive dominant eigenvalue of the next generation matrix. Under the compactness of the next generation operator, we show that R0,n→R0 as n→+∞ in terms of the spectral approximation theory.