DÄ internationalArchive15/2010Basic Reproduction Number
LNSLNS The basic reproduction number according to the formula


(K=population size, beta=transmission rate, alpha=recovery rate, S0=susceptible at the onset of the epidemic, S∞=susceptible at the end of the epidemic) of an infection leading to immunity depends on the size of the exposed population and on the number of people with immunity. Students in school years 8/9 would currently comprehend that infections with a basic reproduction number of 2 and a duration of illness of 10 days would infect an entire urban population of 160 000 within 23 days. But epidemics progress through large populations without infecting every single person. In a school class of 30, which means 30 contacts per student—including the occasional missing student—the resultant basic reproduction number is 1.5, whereas R0 for 100 persons is 2.0 and for 1000 persons, 3.0. Not every infected person therefore equally qualifies for spreading an epidemic with discrete compartments. An elderly person living by themselves will not acquire flu from external contacts, nor will they prolong a chain of infection if they contract influenza. Doctors who look after an average of 1000 patients, however, are effective index patients if they contract flu. Epidemiological models assume that the transmission rate of a causative strain is identical across an entire population. The differences in the observable spread result precisely from this assumption..
DOI: 10.3238/arztebl.2010.0276a

Dr. med. Martin P. Wedig
Roonstr. 86, 44628 Herne, Germany
1.
Wissenbach, F.: Grundlegende Ideen mathematischer Epidemiologie. Seminar zur Analysis, Vortag 2.7.2009, TU Dortmund.
2.
Mikolajczyk R, Krumkamp R, Bornemann R, Ahmad A, Schwehm M, Duerr HP: Influenza—insights from mathematical modelling [Influenza – Einsichten aus mathematischer Modellierung]. Dtsch Arztebl Int 2009; 106(47): 777–82. VOLLTEXT
1. Wissenbach, F.: Grundlegende Ideen mathematischer Epidemiologie. Seminar zur Analysis, Vortag 2.7.2009, TU Dortmund.
2. Mikolajczyk R, Krumkamp R, Bornemann R, Ahmad A, Schwehm M, Duerr HP: Influenza—insights from mathematical modelling [Influenza – Einsichten aus mathematischer Modellierung]. Dtsch Arztebl Int 2009; 106(47): 777–82. VOLLTEXT