# Bivariate collocation methods for computing the basic reproduction number of population dynamics with double structure

The basic reproduction number, commonly known as \(R_0\), is a mathematical tool that plays an important role in the study of population dynamics, in particular in the field of mathematical epidemiology. In this context \(R_0\) measures the average number of secondary cases produced by an infected individual in the hypothesis that the entire population belongs to the class of “susceptible”.

In this thesis we face the problem of extending to the case of double structure the numerical collocation approach proposed in [1] and [2] to approximate \(R_0\) for models of structured population dynamics based on computing \(R_0\) as spectral radius of the so-called Next Generation Operator.

The resulting numerical scheme is then applied to a model structured by age and immunity recently proposed by Francesca Scarabel and Jianhong Wu (York U., Toronto, Canada) for describing pertussis.

This seminar concerns the results of Simone’s MSc thesis (advisor Dimitri Breda, co-advisors Francesca Scarabel and Rossana Vermiglio).

- [1] , Efficient numerical computation of the basic reproduction number for structured populations, J. Comput. Appl. Math., 384 (2021), 113165, DOI: 10.1016/j.cam.2020.113165.
- [2] , Collocation of next-generation operators for computing the basic reproduction number of structured populations, submitted.

The seminar will take place on Microsoft Teams: if you would like to attend, please write to .