Interpreting measures of tuberculosis transmission: a case study on the Portuguese population

Abstract

Background: Tuberculosis remains a high burden for Human society despite considerable investments in its control. Unique features in the history of infection and transmission dynamics of tuberculosis pose serious limitations on the direct interpretation of surveillance data and call for models that incorporate latent processes and simulate specific interventions.

Methods: A transmission model was adjusted to the dataset of active tuberculosis cases reported in Portugal between 2002 and 2009. We estimated key transmission parameters from the data (i.e. time to diagnosis, treatment length, default proportion, proportion of pulmonary TB cases). Using the adjusted model to the Portuguese case, we estimated the total burden of tuberculosis in Portugal. We further performed sensitivity analysis to heterogeneities in susceptibility to infection and exposure intensity.

Results: We calculated a mean time to diagnose of 2.81 months and treatment length of 8.80 months in Portugal. The proportion defaulting treatment was calculated as 0.04 and the proportion of pulmonary cases as 0.75. Using these values, we estimated a TB burden of 1.6 million infected persons, corresponding to more than 15% of the Portuguese population. We further described the sensitivity of these estimates to heterogeneity.

Conclusions: We showed that the model reproduces well the observed dynamics of the Portuguese data, thus demonstrating its adequacy for devising control strategies for TB and predicting the effects of interventions.

Figure 1

Sojourn time distribution in the primary infection state. Exponential distribution for the time infected individuals remain in primary state (P), and proportional progression to active disease (I) and latent (L) states. The curves are given by P(t) = e^{− δ ⋅ t}, I(t) = ϕ ⋅ (1 − e^{− δ ⋅ t}), L(t) = (1 − ϕ) ⋅ (1 − e^{− δ ⋅ t}), with parameter values ϕ = 0.05 and δ = 2 yrs⁻¹, in agreement with the expectation that 5% of primary cases progress to active disease within 2 years of infection (dotted-line).

Figure 2

Superposition of observed data and theoretical expectations. a) Cumulative frequency of detection of tuberculosis infected patients and theoretical expectations for the inflow to class T assuming τ = 4.26 yrs⁻¹. b) Cumulative frequency of TB treatment length and theoretical expectations for the outflow from class T assuming δ_T = 1.36 yrs⁻¹. c) Cumulative frequency of TB treatment defaulters and theoretical expectations for the flow from class T to class I assuming δ_T = 1.36 yrs⁻¹ and ϕ_T = 0.04.

Figure 3

Prevalence of active TB as a function of transmission parameters. Proportion of infectious individuals as a function of β and R₀. Curves represent the endemic equilibria according to the homogeneous system (1) (full line) and the heterogeneous system (3) (dashed line), using parameter values specified in Table 1. Estimates of β and R₀ for the same proportion of infectious individuals under both models are marked (dotted lines).