  In this paper, we introduce a general numerical method to approximate the
reproduction numbers of a large class of multi-group, age-structured,
population models with a finite age span. To provide complete flexibility in
the definition of the birth and transition processes, we propose an equivalent
formulation for the age-integrated state within the extended space framework.
Then, we discretize the birth and transition operators via pseudospectral
collocation. We discuss applications to epidemic models with continuous and
piecewise continuous rates, with different interpretations of the age variable
(e.g., demographic age, infection age and disease age) and the transmission
terms (e.g., horizontal and vertical transmission). The tests illustrate that
the method can compute different reproduction numbers, including the basic and
type reproduction numbers as special cases.
