Modelling the annual risk of tuberculosis infection

Tuberculosis has been declining in developed countries for a long time, as a result of the intrinsic epidemiological characteristics of this disease, combined with improvement in the standard of living and more recently the use of antibiotics. In these low prevalence countries, decisions concerning the objectives of tuberculosis programmes have to be taken and the consequences of short term changes in the sanitary situation have to be assessed.

A deterministic model, without age structure, of the dynamics of pulmonary tuberculosis is proposed. The model extends that of Waaler and is intended to be more suitable for application to developed countries. The flows between seven subgroups of population, based on the natural history of the disease, are modelled and vaccination is taken into account. Values of model parameters and initial prevalences were deduced from published data.

As a first step, qualitative comparisons are performed between the model-predicted decline in the annual risk of infection (ARI) and data from the Netherlands tuberculosis survey. Using parameter values suited to France, our model shows that the predicted decline is slower in France than in the Netherlands; a result which tallies with epidemiological observations. Uses of the model as a decision tool are illustrated in two cases, that of ending systematic BCG vaccination and that of a sudden increase in the number of infectious cases.