rate _λ[t]_ (= _βI[t]_ , usually called the “annual risk of infection”), fraction _f_ develop progressive primary TB within one year of contact. By contrast, fraction 1- _f_ move into the latent class ( _L_ ), from which they breakdown relatively slowly (endogenous reactivation at rate ν ) to active disease. TB can arise from latent infection many years after the infection was acquired. However, the progression from latency to active disease can be accelerated by (exogenous) re-infection, provided re-infection overcomes the partial immunity (measured by proportion _x_ ) acquired from the primary infection.

Active disease is either infectious pulmonary TB ( _I_ , arising in fraction _s_ of cases), in which most patients have a positive-sputum smear on microscopic examination, or noninfectious pulmonary or extrapulmonary TB ( _N_ , fraction 1- _s_ ). Patients with active TB have an elevated death rate, which is higher for infectious ( _μi_ ) than for non-infectious disease ( _μn_ ), and much higher than the mortality rate from all other causes ( _μ_ ). These death rates are expressed in terms of survival (e.g. 1- _μ_ ) from one time step to the next, which allows us to assign different survival rates to patients in the same state but who have with different fates. The notation _[t]_ and _[t-1]_ represents the value of state variables at, respectively, the current and at the previous time step (1 year ago).

Birth and death rates are assumed equal so the total population remains constant. A small proportion of human TB cases are caused by mycobacteria other than _M. tuberculosis_ , especially _M. bovis_ , but they are not relevant to this analysis. More important are the effects of HIV and MDR-TB, which are modeled as extensions of the above equations (not shown here, but see e.g., (Dye and Williams 2000).

Before drugs became available to treat TB in the 1940s, a proportion of patients selfcured. Self-cure is still a part of TB natural history and is represented in this model by _ρ_ . Case-detection rates ( _δ_ ) are different for DOTS (subscript _D_ ) and non-DOTS or other programs (subscript _O_ ). In general, the efficacy of drug treatment (cure, _κ_ ) is higher when administered in DOTS programs than elsewhere. Patients that are cured, either naturally or by drug treatment, move to the recovered class ( _Ri_ or _Rn_ ), where they are assumed to remain (i.e., this version of the model does not allow relapse).

Parameter values used for this investigation are similar to those used in previous modeling analyses (Vynnycky and Fine 1997; Dye, Garnett et al. 1998; Lietman and Blower 2000; Young and Dye 2006), and are given in Table 3. To reconstruct the recent epidemiological history of TB in seven regions of the world (representing the whole world except the established market economies and central Europe), the model was fitted to WHO estimates for incidence, prevalence, and deaths from 1990 (the baseline for the Millennium Development Goals [MDG]) to 2003 (the latest data available at the time of writing the Global Plan). The fitting was carried out principally by adjusting parameters determining the contact rate ( _β_ ) and the natural recovery rate ( _ρ_ ). An example of the fit (for the Western Pacific Region) is illustrated in Figure A.2.

The effect of control is determined by inputs set out in the seven regional plans, as described in Table 11 of Annex 1 to the Global Plan (Stop TB Partnership and World Health Organization 2006). Case detection and cure rates are based on, and extended 28