Bivariate collocation methods for computing the basic reproduction number of population dynamics with double structure
seminari CDLab: laurea magistrale matematica
Simone De Reggi
Università di Udine
Simone De Reggi, laureando magistrale in matematica, terrà un seminario sul suo lavoro di tesi. Se interessati contattate Dimitri Breda per ricevere il link Teams. Segue abstract (oppure qui: http://cdlab.uniud.it/events/seminar-20201008). The basic reproduction number, commonly known as R0, 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 R0 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  and  to approximate R0 for models of structured population dynamics based on computing R0 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).]  D. Breda, F. Florian, J. Ripoll and R. Vermiglio, 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.  D. Breda, T. Kuniya, J. Ripoll and R. Vermiglio, Collocation of next-generation operators for computing the basic reproduction number of structured populations, submitted.