Mathematical models of drug-resistant tuberculosis lack bacterial heterogeneity: A systematic review

Abstract

Drug-resistant tuberculosis (DR-TB) threatens progress in the control of TB. Mathematical models are increasingly being used to guide public health decisions on managing both antimicrobial resistance (AMR) and TB. It is important to consider bacterial heterogeneity in models as it can have consequences for predictions of resistance prevalence, which may affect decision-making. We conducted a systematic review of published mathematical models to determine the modelling landscape and to explore methods for including bacterial heterogeneity. Our first objective was to identify and analyse the general characteristics of mathematical models of DR-mycobacteria, including M. tuberculosis. The second objective was to analyse methods of including bacterial heterogeneity in these models. We had different definitions of heterogeneity depending on the model level. For between-host models of mycobacterium, heterogeneity was defined as any model where bacteria of the same resistance level were further differentiated. For bacterial population models, heterogeneity was defined as having multiple distinct resistant populations. The search was conducted following PRISMA guidelines in five databases, with studies included if they were mechanistic or simulation models of DR-mycobacteria. We identified 195 studies modelling DR-mycobacteria, with most being dynamic transmission models of non-treatment intervention impact in M. tuberculosis (n = 58). Studies were set in a limited number of specific countries, and 44% of models (n = 85) included only a single level of "multidrug-resistance (MDR)". Only 23 models (8 between-host) included any bacterial heterogeneity. Most of these also captured multiple antibiotic-resistant classes (n = 17), but six models included heterogeneity in bacterial populations resistant to a single antibiotic. Heterogeneity was usually represented by different fitness values for bacteria resistant to the same antibiotic (61%, n = 14). A large and growing body of mathematical models of DR-mycobacterium is being used to explore intervention impact to support policy as well as theoretical explorations of resistance dynamics. However, the majority lack bacterial heterogeneity, suggesting that important evolutionary effects may be missed.

Fig 1. PRISMA flow diagram outlining the systematic selection of studies to include in the analysis.

Fig 2. Uneven geographical distribution of mathematical models of DR-mycobacteria (a) and correspondence with MDR/RR-TB incidence (b).

(a) Countries captured in models of DR-mycobacteria. Note: some models include outputs for multiple countries, therefore this image represents all countries modelled, not the total number of models. (b) From the WHO Global Tuberculosis Report 2022 [1], the 10 countries with the highest estimated MDR/RR-TB incidence are given with number of models in brackets. The colours in the table match the corresponding colours of the country in part (a). Map layer made with Natural Earth, free vector and raster map data @ naturalearthdata.com.

Fig 3. Model aims broken down by model types (colours) highlights transmission models are the most used for DR-mycobacteria modelling.

The model type (colours) definitions can be summarised as follows: [1] Bacterial dynamics: Capture bacterial populations without considering between-host transmission. [2]; Decision analytic: Track cohorts of human individuals through treatment or diagnostic pathways without ongoing transmission. [3] Pharmacokinetic/pharmacodynamic (PK/PD): Focus on drug concentrations and their effects in vivo, incorporating parameters related to bacterial populations. [4] State Transition: Involve individuals or populations transitioning between different disease states, with the force of infection as a static input parameter. [5] Statistical: inference-based models of collected or population data. [6] Transmission: Dynamically account for the spread of bacteria between individuals or populations. [7] Operational models: simulation of patient pathways and treatment or diagnostic procedures. The model aim (x axis) definitions can be summarised as follows: (1) Non-treatment Interventions: Model the impact of interventions not related to changes in antibiotic usage or treatment without considering economic aspects. (2) Non-treatment Interventions + cost-effectiveness: Model the impact of interventions not related to changes in antibiotic usage or treatment while considering their economic impact. (3) Treatment interventions: Model interventions related to changes in antibiotic usage. (4) Treatment interventions + cost-effectiveness: Model interventions related to changes in antibiotic usage while considering their economic impact. (5) Parameter estimation: Estimate parameters by comparing to data, trends, or varying model structures or components. (6) Burden estimation models: Quantify the number of individuals potentially infected with DR-mycobacteria. (7) Theoretical models: Theoretically explore interactions between susceptible and resistant strains. Note: "CE" stands for cost-effectiveness. For full details of aim and model type see S2 Text.

Fig 4. Treemap of specific resistance classes included in models in stage 1 shows that the majority of models included MDR/RR and few included more than two resistance classes.

Each coloured cell represents a specific combination of resistances included in a model, with the size of the cell representing how many models included this combination of resistances. “Single” and “Multiple” sections refer to the number of antibiotic resistances included in a model, with “Multiple” referring to models that captured resistance to more than one antibiotic. "*" indicates the model included all possible combinations of antibiotic resistance listed. A = INH, RIF, MDR/RR, MOX, PZA, BDQ, PA, RIF + MOX, RIF + PZA, B = INH, RIF, MDR/RR, AMI, MOX, BDQ, RIF + MOX, RIF + AMI, RIF + BDQ, C = INH, RIF, MDR/RR, XDR, MDR + FQ, MDR + SLInject, D = INH, RIF, MDR/RR, XDR, Pre-XDR. Antibiotic abbreviations as follows: AMI = amikacin, BDQ = bedaquiline, CLR = clarithromycin, ETM = ethambutol, FQ = undefined fluoroquinolone, MOX = moxifloxacin, PA = pretomanid, PZA = pyrazinamide, STR = streptomycin, INH = isoniazid, RIF = rifampicin, MDR/RR = multidrug resistant/rifampicin resistant, XDR = extensively drug-resistant, SLInject = second line injectable antibiotic (from WHO guidelines 2014). S1 Fig shows all resistance categories per 195 models.

Fig 5. Classifications of models including heterogeneity in their bacterial population (Stage 2) were split into bacterial population and between-host models and then stratified by whether they considered single or multiple resistance classes.