Numerical approximation of the basic reproduction number for a class of age-structured epidemic modelsNumerical 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 Ro, 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, R-0 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 R-0,R-n,R-, 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 R-o,R-n -> R-0 as n -> +infinity in terms of the spectral approximation theory.