Data-driven model for the assessment of Mycobacterium tuberculosis transmission in evolving demographic structures

Abstract

In the case of tuberculosis (TB), the capabilities of epidemic models to produce quantitatively robust forecasts are limited by multiple hindrances. Among these, understanding the complex relationship between disease epidemiology and populations' age structure has been highlighted as one of the most relevant. TB dynamics depends on age in multiple ways, some of which are traditionally simplified in the literature. That is the case of the heterogeneities in contact intensity among different age strata that are common to all airborne diseases, but still typically neglected in the TB case. Furthermore, while demographic structures of many countries are rapidly aging, demographic dynamics are pervasively ignored when modeling TB spreading. In this work, we present a TB transmission model that incorporates country-specific demographic prospects and empirical contact data around a data-driven description of TB dynamics. Using our model, we find that the inclusion of demographic dynamics is followed by an increase in the burden levels predicted for the next decades in the areas of the world that are most hit by the disease today. Similarly, we show that considering realistic patterns of contacts among individuals in different age strata reshapes the transmission patterns reproduced by the models, a result with potential implications for the design of age-focused epidemiological interventions.

Keywords: dynamics population; epidemiological models; global health; infectious disease transmission; tuberculosis.

Fig. 1.

Model description. (A) Natural history scheme of the TB spreading model. D, (untreated) disease; F, failed recovery; L, latent; R, recovered; S, susceptible; T, (treated) disease. Types of TB considered: np, nonpulmonary; p+, pulmonary smear positive; p–, pulmonary smear negative. Treatment outcomes: F, treatment failure; $R_D$, default (abandon of treatment); $R_N$, natural recovery; $R_S$, successful treatment. (B) Scheme of the coupling between TB dynamics and demographic evolution. The transmission model summarized in A describes the evolution of the disease in each age group, including the removal of individuals due to TB mortality (curved arrows). The evolution of the total volume of each age stratum is corrected (bidirectional arrows: TB-unrelated population variations) to make the demographic pyramid evolve according UN prospects. (C) Empirical contact patterns used for African and Asian countries. (D) Data flow scheme. Epidemiological parameters, contact matrices, and demographic prospects are used to calibrate the model, with the goal of reproducing observed TB incidence and mortality trends during the period 2000–2015. As a result of model calibration, scaled infectiousness, diagnosis rates, and initial conditions of the system in 2000 are inferred. These elements are then used (along with epidemiological parameters, contacts, and demographic data) to extend model forecasts up to 2050. For further details regarding model formulation and calibration, the reader is referred to SI Appendix.

Fig. 2.

Population structure at 2000 and 2050 (projection) and annual incidence and mortality rates predicted by our model in 2000–2050 for Ethiopia, Nigeria, India, and Indonesia. Colored areas represent 95% confidence intervals. The contribution to overall uncertainty that stems from each of the four types of input data is disclosed. (Contributions are cumulative.)

Fig. 3.

Effects of demographic dynamics on model forecasts. (A) Incidence rates from 2000–2050 obtained from the full model (red) and reduced model 1 (constant demography, blue). Relative variation in incidence in 2050: full vs. reduced model 1: India, 39.6% (13.9–63.6, 95% CI); Indonesia, 23.4% (7.9–36.6, 95% CI); Ethiopia, 56.0% (29.2–62.1, 95% CI); Nigeria, 34.5% (9.1–42.9, 95% CI). (B) Relative variation of aggregated incidence at 2050 for the top 12 countries with highest absolute TB burden in 2015 vs. variation in the fraction of adults in the population during the period 2000–2050. In all countries but Tanzania and The Philippines, in gray, the variations in incidence are significant at a nominal P = 0.05. (C) Age-specific average incidence rate of TB vs. variation of age-strata population density in 2000–2050. Older individuals are, at the same time, those affected by higher TB incidence rates and those whose presence in the population is increasing as a result of populations’ aging. (D) Incidence projections for synthetic scenarios of demographic evolution, including transition toward younger populations (iii–i and iii–ii), static populations (iii remaining constant), and realistic transitions representing populations’ aging (from iii to iv and from iii to v). Pivotal demographic structures corresponding to stages i, iii, and v are taken from actual examples (Ethiopia in 2000, Indonesia in 2000, and China in 2050) and normalized to a common total population to rule out hypothetical system volume effects. Stages ii and iv are obtained upon linear interpolation. In each panel, the demographic evolution of each country is substituted by these synthetic scenarios: demographic transitions that go from stage iii in 2000 to different ending points in 2050. Colors in incidence series correspond to those in the arrows below, indicating the respective demographic transitions. Model calibration is repeated in each case.

Fig. 4.

Age-to-age infection rate matrices (number of infections from age group a to age group a′ per year per million people in target age-group a′) and age-specific infection and incidence rates forecasted in 2050 for India and Ethiopia (number of contagions or new active TB cases, respectively) per year and million individuals in a given age group. (Left column) The forecasts derive from the full model. (Center column) The forecasts derive from reduced model 1 (constant demography). (Right column) The difference (full model minus reduced model 1) of these three observables: infection matrices, age-specific infection rates, and age-specific incidence rates. Differences in incidence and infection rates are shown in gray when they are not statistically significant. Neglecting demographic dynamics appears associated to an underestimation of infections caused by adults in both countries and an overestimation of infections from children, mostly in India (infection matrices). At the level of infection/incidence rates (histograms), the full model produces larger age-specific infection and incidence rates than the reduced version, more intensely among adults.

Fig. 5.

Age-to-age infection rate matrices and age-specific infection and incidence rates forecasted in 2050 for India and Ethiopia, from the full model (Left column) and reduced model 2 (Center column), with the difference (full model minus reduced model 2) (Right column) shown in each case. Differences in incidence and infection rates are shown in gray when they are not statistically significant; otherwise they have the color associated to the model for which the rate is higher. When empirical contact patterns are introduced in the model, we observe an increased density of infections close to the diagonal (i.e., contagions taking place between individuals of similar age) and fewer infections taking place from children to adults or vice versa. At the level of infection/incidence rates, this translates into an underestimation of burden among adults (and an overestimation among children) associated to assuming contacts homogeneity in the reduced model.