[Mathematical models used in the study of infectious diseases]

Infectious diseases have historically had a large impact on morbidity and mortality, which probably led predictions about the evolution of epidemics have been made for centuries. The objective is to identify the most-frequently used mathematical models and the diseases to which they are applied.

Publications indexed in Medline between 1 January 2000 and 31 August 2009 were reviewed: each abstract was read and articles that did not comply with the objectives of the study were discarded. The type of infectious disease, the mathematical model applied, the statistical technique used, the model of transmission and the country of the first author were collected.

Of 617 possible articles, 162 were finally selected. The evolution of articles by years shows a rising trend since 2005. The most-common disease types were unespecified infectious diseases, HIV-AIDS, malaria and tuberculosis. Among mathematical models there was a predominance of stochastic models. The most-common country of the first author included the European countries, especially UK and USA. The most-widely used model of transmission was the SIR model (21 cases/45l). Of the 58 articles which identified a statistical technique, 12 (20.7%) used generalized linear models and 11 (19.0%) used Markov models.

There is growing interest in the modelling of communicable diseases and substantial innovations may be expected in forthcoming years, above all if their use is extended and applied to "forgotten" communicable diseases or other health problems.