The paper has illustrated the use of mathematical model (epidemetric model) for the prediction of the trend of tuberculosis in a given situation with or without the influence of specific tuberculosis control programme. The paper also advocates the use of models for evolving applicable control measures by reflecting their interference in the natural trend of tuberculosis in control areas. These models were constructed by applying methods which have been developed and utilised in other social sciences.
The precise estimates of the various parameters entering the model must be available if realistic long term results are to be achieved through model methodology. The need for exact data regarding prevalence and incidence of infection and disease, necessitates longitudinal surveys in large random population groups. It is, however, the present authors firm opinion that it would be fruitful for almost any health department, to compare their best available epidemiological knowledge in a system of relationships in order to quantify their concept of the situation. Such an exercise in mathematics would, in any case, serve to sharpen the epidemiologists thinking and would lead them to appreciate what data they need most urgently. The model may help in predicting the trend of tuberculosis in a given situation.

This paper estimates the natural trend of tuberculosis in rural south India and the potential epidemiological impact of a few selected programmes on this trend, by using the values of important variables and parameters derived from a longitudinal epidemiological study conducted in 1961-68 in Bangalore district by the National Tuberculosis Institute (NTI), Bangalore. The values are fed into an epidemetric model and the final outputs of computerization derived are incidence of disease (in both absolute and relative terms) and cumulative future prevalence of disease.

(1) An annual average input of new generations of 3.16% has been derived for a population of 1 million by using a simplified fertility rate formula. A constant reduction 0f 1% per year has been assumed until fertility rate has reached 50% of its starting value. The assumption is that any reduction in fertility due to current family planning programmes will have a considerable impact on the size of the population and on the epidemiological situation. Further demographic assumptions are, excess mortality applied to groups of active cases and fatality among untreated cases. (2) The population is subdivided into the following epidemiological groups: (i) non-infected, (ii) infected for – (a)< 5 years, (b)= 5 years, (iii) protected by BCG, (iv) active cases - (a) non-infectious, (b) infectious and (v) previous cases. Initially groups (iii) and (v) are given zero values. The future risk of infection is adjusted to the force of infection, which is assumed to be reduced to 1/7th when a case is successfully treated. Morbidity rates include transfers from infected group to active cases group during 5 year periods. (3) A spontaneous healing rate of 50% and a cure rate of 80% after chemotherapy are assumed. Protective effect of BCG is given three values: 30%, 50% and 80%, with uniform annual reduction of 1% (4) Case detection and treatment (CF/T) is given two values: 66% and 20%. Coverage for BCG limited to 0-20 years is assumed to be 66% or 30%.

The computer simulation output for natural trend shows that the absolute number of new cases increases considerably while the incidence rate do not warrant firm conclusions about any long term trend. All programmes considered have considerable potential impact. The CF/T programmes will reduce the incidence after 25 years by only 12% compared to reduction of 17% by the BCG programme. In general, the effect of CF/T will be more immediate and of BCG will be seen much later. To avoid the drawbacks of incidence as an indicator of tuberculosis situation, the cumulated future prevalence is taken as the tuberculosis problem. To adjust for the present significance of future cases as part of the problem certain discount rate have been applied. The CF/T programme and the BCG programme with 50% protection lead to 69% problem reduction, if not discounted. With increasing discount rates, CF/T has an advantage over BCG. The actual problem reduction will be higher than that estimated if improvements in the standard of living are expected during the coming years.

In conclusion, data on the dynamics of tuberculosis situation in rural south India, obtained by NTI, Bangalore when fed into a mathematical model, many predictions about the future tuberculosis situation were made under a wide range of hypothetical assumptions.