title: Influenza--insights from mathematical modelling.
abstract: BACKGROUND
  When the first cases of a new infectious disease appear, questions arise about the further course of the epidemic and about the appropriate interventions to be taken to protect individuals and the public as a whole. Mathematical models can help answer these questions. In this article, the authors describe basic concepts in the mathematical modelling of infectious diseases, illustrate their use with a simple example, and present the results of influenza models.
  
  
  METHODS
  Description of the mathematical modelling of infectious diseases and selective review of the literature.
  
  
  RESULTS
  The two fundamental concepts of mathematical modelling of infectious diseases-the basic reproduction number and the generation time-allow a better understanding of the course of an epidemic. Modelling studies based on past influenza epidemics suggest that the rise of the epidemic curve can be slowed at the beginning of the epidemic by isolating ill persons and giving prophylactic medications to their contacts. Later on in the course of the epidemic, restricting the number of contacts (e.g., by closing schools) may mitigate the epidemic but will only have a limited effect on the total number of persons who contract the disease.
  
  
  CONCLUSIONS
  Mathematical modelling is a valuable tool for understanding the dynamics of an epidemic and for planning and evaluating interventions.
authors.affiliation: Fakultät für Gesundheitswissenschaften, Universität Bielefeld, Bielefeld. mikolajczyk@uni-bielefeld.de
authors.forename: Rafael
authors.initials: R
authors.lastname: Mikolajczyk
authors.forename: Ralf
authors.initials: R
authors.lastname: Krumkamp
authors.forename: Reinhard
authors.initials: R
authors.lastname: Bornemann
authors.forename: Amena
authors.initials: A
authors.lastname: Ahmad
authors.forename: Markus
authors.initials: M
authors.lastname: Schwehm
authors.forename: Hans-Peter
authors.initials: HP
authors.lastname: Duerr
mesh_terms: D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D005858:Germany / Q000453:epidemiology; D006801:Humans; D015994:Incidence; D007251:Influenza, Human / Q000453:epidemiology*; D008954:Models, Biological; D011159:Population Surveillance; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods; D012307:Risk Factors