caa a22 4500 445330481 CHVBK 20180317142735.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00285-010-0354-8 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0354-8 Genealogy with seasonality, the basic reproduction number, and the influenza pandemic [Elektronische Daten] [Nicolas Bacaër, El Ait Dads] The basic reproduction number R 0 has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years. The definition involves the spectral radius of an integral operator. As in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. In this paper we show that R 0 for periodic models is still an asymptotic per generation growth rate. We also emphasize the difference between this theoretical R 0 for periodic models and the "reproduction number” obtained by fitting an exponential to the beginning of an epidemic curve. This difference has been overlooked in recent studies of the H1N1 influenza pandemic. Springer-Verlag, 2010 Basic reproduction number nationallicence Seasonality nationallicence Epidemics nationallicence H1N1 influenza nationallicence Bacaër Nicolas Research group UMMISCO, IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy, France aut Ait Dads El Laboratoire de Mathématiques et Dynamique des Populations, Université Cadi Ayyad, Marrakech, Morocco aut Journal of Mathematical Biology Springer-Verlag 62/5(2011-05-01), 741-762 0303-6812 62:5<741 2011 62 285 https://doi.org/10.1007/s00285-010-0354-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0354-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bacaër Nicolas Research group UMMISCO, IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy, France aut NATIONALLICENCE 700 1- Ait Dads El Laboratoire de Mathématiques et Dynamique des Populations, Université Cadi Ayyad, Marrakech, Morocco aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/5(2011-05-01), 741-762 0303-6812 62:5<741 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer