Abstract

PAVA, Elmer de la; SALGUERO, Beatriz  and  ALZATE, Alberto. A mathematical model of the annual risk of tuberculosis infection in Cali, Colombia. Rev Panam Salud Publica [online]. 2002, vol.11, n.3, pp. 166-171. ISSN 1020-4989.  http://dx.doi.org/10.1590/S1020-49892002000300005.

Objective. The annual risk of infection (ARI) for tuberculosis is the probability that an individual without previous contact with the tubercle bacillus has of being infected during the course of a year. The ARI is the most appropriate indicator for estimating the degree of tuberculosis infection in a population. The objective of this paper was to estimate the ARI and its trends in the city of Cali, Colombia, using data provided by the Municipal Secretariat of Health. Methods. We used a deterministic model of the dynamics of pulmonary tuberculosis. The flows among the population subgroups were based on the natural history of the disease, taking vaccination into account. Using the data from the Municipal Secretariat of Health, we estimated the initial conditions and the values of the parameters. Results. The mean ARI values were 1.24% in the 1970s, 0.93% in the 1980s, and 0.85% in the 1990s. In order to assess trends, we attempted to predict the annual risk, utilizing a nonlinear least-squares adjustment of the data on the overall percentage for each year. With that approach, we projected that the ARI in 2003 would be 1.3%, indicating a return to the patterns found in the 1970s. Conclusions. The estimated risk of tuberculosis infection in Cali during the decades of the 1970s, the 1980s, and the 1990s was very high in comparison with the risk in countries such as the Netherlands, which in 1985 had an ARI of 0.012%. However, the ARI in Cali is not so high in comparison to indices for other countries of South America, which range from 0.5% to 1.5%. This model and the simulation it produced showed a rising trend in the ARI for Cali, as well as demonstrated that the ARI will tend to continue to rise if control measures are not improved.

Keywords : Tuberculosis; riesgo anual de infección; modelos matemáticos.