# Numerical computation of the basic reproduction number in population dynamics

The basic reproduction number, or \(R_0\), is a quantity defined in ecology and epidemiology as a means to investigate what formally are the properties of stability of the zero solution of a linear system of equations.

In most modern models the population is structured, i.e. individuals’ fertility and mortality are differentiated by some properties, like age, sex, or dimension; in those models the basic reproduction number is characterized as the spectral radius of an operator, called next generation operator.

Despite the importance of this quantity, and the number of works devoted to its applications in epidemiology, the only attempt to develop an algorithm for its numerical computation was carried out in [1].

We thus focus on the numerical computation, and in particular on an algorithm which is more general, and more accurate than the existing one for equal computing resources.

This seminar concerns the results of Francesco’s MSc thesis.

- [1] , Numerical approximation of the basic reproduction number for a class of age-structured epidemic models, Appl. Math. Lett., 73 (2017), pp. 106–112, DOI: 10.1016/j.aml.2017.04.031.