Catalytic model

Catalytic models characterise the population dynamics of exposure to infection from birth and throughout life from cross-sectional prevalence data⁹. The annual force of infection, the rate at which susceptible individuals acquire an infection or reinfection, can be estimated from these models. By convention, TB ‘infection’ implies immunoreactivity (interferon gamma release assay [IGRA] or tuberculin skin test [TST] positivity) and so for clarity the term ‘rate of exposure’ will be used hereafter to refer to the rate at which the collected bioaerosol sample from an individual converts from undetectable to detectable Mtb.

Using a reverse catalytic model, we derived estimates of the rate of exposure based on empirically measured age-specific prevalence in healthy individuals and informed by empirical data indicating reversion rate. The model relates the prevalence, P, at age, a, to rate of exposure, λ, and rate of reversion, ρ (see Eq. 1 & Fig. 1). We assumed that respiratory bioaerosol from individuals at birth have no detectable Mtb, that all individuals are susceptible and that the rate of exposure remains constant through calendar time. We interpret loss of Mtb detection in exhaled aerosol samples as clearance of Mtb from the respiratory airway compartment. Also, conversion to aerosol Mtb positivity is assumed to be due to external exposure to airborne Mtb and not a fluctuating positivity based on cyclical underlying TB disease (unlikely for the vast majority of randomly selected individuals). For the primary analysis, the rate of exposure, λ, and rate of reversion, ρ are both assumed to be constant throughout life and homogenous across the community and consequently that the population reaches a steady prevalence.

Reverse catalytic model fitted to age-specific bioaerosol positivity prevalence data, P(a) with \(\lambda\) as the rate of exposure and \(\rho\) as the rate of reversion. The pre-factor \(\frac{\lambda }{\lambda +\rho }\) gives the saturating prevalence.

The average age at which Mtb is first identified in an individual’s bioaerosol is given by 1/ \(\lambda\) and the average duration of Mtb persistence is 1/ \(\rho\).

Data sources

TB aerobiology study and sample collection

The Aerobiology and TB Research Unit in Cape Town, South Africa has recently published studies demonstrating the detection of Mtb in captured respiratory bioaerosol from a broad range of individuals spanning the TB disease spectrum^2,3. In brief, the sampling methodology involved a modified respiratory aerosol sampling chamber (RASC) which consists of a HEPA-filtered enclosure accommodating a single individual (see Supplementary information). The seated participant places their head into a metallic elliptical cone through which a unidirectional airflow is created by a high-flow (300L per minute) cyclone collector connected at the cone apex. Respiratory bioaerosol is extracted into sterile phosphate-buffered saline (PBS) through inertial impaction. The high velocity airflow (12 ms⁻¹) enables efficient collection even of aerosols generated during explosive respiratory activities such as coughing. A study nurse directs the participant to complete a 15-min sampling protocol comprising 5-min sampling for each of 15 forced vital capacity manoeuvers (FVCs), tidal breathing, and 15 voluntary coughs. Each sample collection was processed in the on-site laboratory. After centrifugation the pellet was resuspended in 200μL Middlebrook 7H9 medium and incubated overnight with the DMN-trehalose probe¹⁰. Washed samples were added to a nanowell device⁵ which was sealed and centrifuged before visualization by fluorescence microscopy. Experienced microscopists determined the presence of Mtb based on the morphology and fluorescence staining characteristics of the bacilli⁵. Each sample was assessed by two microscopists who were blinded to participant or empty chamber controls. Counts of visualized bacilli were made, however, for the purposes of this study results are interpreted in binary fashion i.e. any Mtb bacillus detected or none detected.

Respiratory bioaerosol Mtb prevalence data

Age-specific prevalence profiles of Mtb bioaerosol positivity were constructed from cross-sectional sampling data of healthy individuals from a highly TB burdened South African peri-urban community 40 km south-west of Cape Town collected between February 2022 and December 2022. Erfs (land parcels) were randomly selected from the community and all individuals living on the erf were offered entry into the study. 135 individuals underwent sampling with ages ranging from 14–72 years (mean 33 and standard deviation 13) and 64% female.

Respiratory bioaerosol Mtb clearance rate

In conjunction, data from a recently published study² with longitudinal bioaerosol sampling of TB clinic attendees, collected between May 2020 and May 2022, at baseline and approximately 2-weeks, 2-months and 6-months from the same community were evaluated to determine rates of bioaerosol clearance. Those in the non-TB diagnosed group (“Group C” as described in the aforementioned study²) who did not receive treatment (n = 30) were aged between 15–67 (mean age 40 standard deviation 12) and 63% male. The clearance rate was indistinguishable from those on treatment and so the combined result was used to establish a reversion rate.

Statistical analysis

A Bayesian inference approach was used to fit the reverse catalytic model to the bioaerosol sampling data of healthy individuals using Markov chain Monte Carlo (MCMC) with the Gibbs sampling algorithm¹¹. Estimates of parameter posterior distributions were informed by uniform prior distributions for \(\lambda\) and \(\rho\). Observational data from symptomatic individuals² informed the prior for the rate of reversion, \(\rho\), given by:

Therefore, a clearance half-life of 83 days with a 95% confidence interval (CI) of 63–167 days gives a reversion rate of 3.0/year (95% CI 1.5–4.0). The prior for \(\rho\) was therefore chosen as a uniform distribution between 1.5 and 4.0. A relatively non-informative prior with a uniform distribution between 0 and 10 was used for \(\lambda .\) All analyses were performed using R version 4.3.1 and the models were implemented using the RJags package (version 4–14)¹².

MCMC convergence was evaluated by the Gelman-Rubin statistic with a threshold of < 1.1 and the effective sample size (ESS), which is the estimated number of independent samples discounting autocorrelation generated by the MCMC run, with an ESS of > 200 used.

Sensitivity analyses

Bioaerosol prevalence

The data for this study are limited to a single community in Cape Town, South Africa and therefore we sought to examine the strength of our findings by conducting sensitivity analyses of all the key parameters. The South African TB incidence is estimated at 615 per 100,000⁷ and the population sampled is from a highly burdened region within South Africa. The main sensitivity analysis was therefore performed to account for settings where a lower bioaerosol positivity prevalence would be expected with data simulated to give mean prevalence of 0.1, 0.2, 0.3 and 0.4. These data were then fitted to the reverse catalytic model.

Age-varying rate of exposure

The baseline reverse catalytic model assumed a time-constant \(\lambda\) without variation by age. However, studies using cross-sectional surveys of TST from the same setting have shown an age-variable force of infection with a peak in the mid-teens and significantly lower in infancy¹³. It is plausible therefore that exposure leading to detectable Mtb in respiratory bioaerosol follows a similar pattern. We modelled the impact on estimates of \(\lambda\) by assuming a \(\lambda\) of zero from ages 1 to 10 and then a uniform prior between 0 and 10 for all ages above 10.

Long-term persistence of Mtb aerosol positivity

The rate of reversion was taken from sampling data from individuals who were symptomatic, it is conceivable therefore that loss of Mtb aerosol positivity is far less frequent or negligible in healthy (untreated) individuals. To examine this possibility a model without reversion (see Eq. 3) was fitted to the prevalence data with comparison to the primary analysis through visual inspection (comparison of model output with superimposed cross-sectional prevalence data) and the Watanabe-Akaike Information Criterion (WAIC)—a measure which balances model complexity with goodness of fit.

Ethics statement

The Human Research Ethics Committee (HREC/REF: 529/2019) of the University of Cape Town approved the studies which generated the data that informed this study.