Here is an interesting evaluation of a tuberculosis control programme in London. The title says it all - it's the Find and Treat service. Table 1 in the paper shows that very few patients are lost to follow up if referred to the service early (though confusingly only 60 - 70% seem to complete treatment: or maybe I've misunderstood that row in the Table.)
Tuberculosis is particularly common among groups particularly likely to default from treatment: the paper cites prevalences of
"788 per 100 000 in homeless people, 354 per 100 000 in people with problematic drug use, and 208 per 100 000 in prisoners. By comparison, the overall prevalence of tuberculosis in London was 27 per 100 000 people"
And outside London prevalence is likely to be even lower - for example the incidence cited in a recent report for Surrey was 7 per 100 000 (albeit with some worries about underreporting). (Note that some of these figures are for incidence and some for prevalence. Incidence you get from reporting or notification of new cases, which should be available everywhere; prevalence estimates require a special survey, or some assumptions about the relationship between incidence and prevalence.)
But back to the economics. The paper uses a model, which hinges on transition probabilities between different compartments, for example between being treated and being lost to follow up , or between being treated and being cured. This concept of transition probabilities between different states is very common in economic modelling. Sometimes costings in economic papers are bold guesses but here we seem to have accurate budget figures. The effect of the programme is estimated in years of life and gain in quality, using the standard metric of an EQ-5D score converted into a utility.
And there is a happy outcome after all this modelling - the service comes in under NICE's cutoff of £30k per QALY.