  As widely known, the basic reproduction number plays a key role in weighing
birth/infection and death/recovery processes in several models of population
dynamics. In this general setting, its characterization as the spectral radius
of next generation operators is rather elegant, but simultaneously poses
serious obstacles to its practical determination. In this work we address the
problem numerically by reducing the relevant operators to matrices through a
pseudospectral collocation, eventually computing the sought quantity by solving
finite-dimensional eigenvalue problems. The approach is illustrated for two
classes of models, respectively from ecology and epidemiology. Several
numerical tests demonstrate experimentally important features of the method,
like fast convergence and influence of the smoothness of the models'
coefficients. Examples of robust analysis of instances of specific models are
also presented to show potentialities and ease of application.
