Influenza--insights from mathematical modelling.
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.
Mikolajczyk
Rafael
R
Fakultät für Gesundheitswissenschaften, Universität Bielefeld, Bielefeld. mikolajczyk@uni-bielefeld.de
Krumkamp
Ralf
R
Bornemann
Reinhard
R
Ahmad
Amena
A
Schwehm
Markus
M
Duerr
Hans-Peter
HP
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