Rationale of the study

Given the increasing use of mathematical models to examine STH transmission and control strategies, a systematic characterization of the existing modelling literature is needed. Existing reviews have largely focused on broader aspects of neglected tropical disease (NTD) control [24–28], without specifically synthesizing STH transmission models according to their biological and structural characteristics, the interventions represented within them, the operational incorporation of WHO roadmap targets, and reported projected timelines. Consequently, the distribution of existing STH models across model and intervention characteristics, the ways in which WHO-defined quantitative targets or programme criteria are incorporated into model specification or analysis, and the extent to which projected timelines are reported have not been systematically characterized. A systematic review using a pre-defined protocol and PRISMA-guided methods provides a structured approach for addressing these questions.

This review aimed to: (i) systematically classify STH transmission models according to their biological and structural characteristics; (ii) decompose STH control interventions represented in mathematical models into orthogonal components and systematically classify them using these components; and (iii) examine the operational incorporation of WHO 2011–2020 and 2021–2030 roadmap targets and summarize the projected timelines reported by the included studies.

This review contributes to the STH modelling literature by providing a structured taxonomy of mathematical models according to transmission unit, mathematical framework, and population structure; systematically classifying interventions according to intervention strategy, delivery platform, target-population representation, and treatment regimen; examining the operational incorporation of WHO roadmap targets and reported projected timelines; and characterizing methodological features of the reviewed modelling literature.

The study is guided by the following three interconnected research questions:

1. Model taxonomy: How are STH transmission models classified according to their biological assumptions, mathematical formulation, and demographic structure?
2. Intervention taxonomy: How are STH control interventions represented in mathematical models classified according to intervention strategy, delivery platform, target-population representation, and treatment regimen?
3. WHO target alignment and reported timelines: How are WHO-defined quantitative targets or programme criteria operationally incorporated into STH model specification or analysis, and what projected timelines are reported by the included studies?

Information sources and search terms

A comprehensive literature search was conducted for peer-reviewed articles published between January 2015 and December 2024 in three bibliographic databases: Web of Science, Embase, and Scopus. Additional studies were identified through manual screening of the reference lists of included articles and relevant systematic reviews.

The search strategy was structured around three core conceptual domains: model terms, intervention terms, and disease terms. Boolean operators were used to combine these domains, yielding a standardized search string of the form:

(“mathematical model*”) AND (“soil-transmitted helminth*”) AND (“control strateg*”)

The asterisk (*) was used as a truncation operator to capture word variants. Synonyms and related terms were incorporated to increase search sensitivity. The complete database-specific search strategies are provided in the Supporting Information (S2 File).

Eligibility criteria

The search was restricted to studies published between 2015 and 2024 to capture recent advances in mathematical modelling relevant to STH morbidity control and transmission interruption. This ten-year window ensures alignment with current global health priorities, particularly the WHO roadmaps for 2011–2020 and 2021–2030, while maintaining a manageable scope.

The inclusion criteria were:

1. a Mathematical models of STH transmission dynamics, including differential equation models (ordinary, partial, or delay), difference equation models, individual-based models, stochastic process models, and hybrid approaches.
2. b Models evaluating one or more STH control strategies.
3. c Studies reporting STH model-based outcomes such as infection prevalence, intensity, or elimination thresholds.
4. d Peer-reviewed journal articles published in English between January 2015 and December 2024.

The exclusion criteria were:

1. a Non-dynamic STH models (example purely statistical analyses, regression models, or machine learning approaches without transmission dynamics).
2. b Studies focusing exclusively on cost-effectiveness without incorporating transmission dynamics.
3. c Diagnostic-focused models addressing only test performance without evaluating transmission or interventions.
4. d Models of helminth species other than STH.
5. e Any study that does not evaluate STH control interventions.
6. f Grey literature (such as dissertations, reports, conference proceedings, abstracts, letters, books, and book chapters).
7. g Within-host or pharmacological models lacking population-level transmission dynamics.

Study selection and consistency check

All records retrieved from the databases were imported into EndNote by a single investigator (LM) for duplicate removal and reference management, and subsequently transferred to the Systematic Review Accelerator for additional duplicate screening. The database search identified 597 records, with an additional 14 records obtained through reference list screening, yielding a total of 611 records (see S3 File). After removal of 84 duplicates, 527 unique articles remained for screening.

Screening was conducted in two stages by five reviewers (LM, MA, SM, IM, SK). In the first stage, three reviewers (LM, MA, SM) independently screened titles and abstracts of all 527 records against the predefined eligibility criteria. Of these, 444 were excluded, and 83 articles were retained for full-text review. In the second stage, two reviewers (IM, SK) independently assessed the full texts, excluding 41 studies and yielding 42 studies for inclusion. Discrepancies at any stage were resolved through discussion, with a third reviewer consulted where necessary. The study selection process is illustrated in the PRISMA flow diagram (Fig 1).

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Fig 1. PRISMA schematic diagram showing study selection process.

Database searches yielded 597 records; reference searches added 14 records. After removing 84 duplicates, 527 records were screened, 444 excluded, 83 full-text articles assessed, 41 excluded, and 42 studies finally included.

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Data extraction process, coding of framework, and data synthesis

Data extraction was conducted using Microsoft Excel. The 42 included studies were distributed among five authors: two authors extracted data from nine studies each, and three authors extracted data from eight studies each (LM: 9, MA: 9, SM: 8, IM: 8, SK: 8). Extraction was performed independently between March 2 and March 25, 2025. Furthermore, a reviewer (LM) independently verified a random 10% sample of the extracted data to ensure accuracy. The complete extraction file, including all variables and extractor information, is provided in S4 File.

To ensure consistent classification across heterogeneous studies, we developed and applied a structured coding framework covering model characteristics, intervention characteristics, and the operational incorporation of WHO roadmap targets and reported timelines. Classification categories were defined a priori for the principal model and intervention dimensions, with mutually exclusive study-level categories applied where specified. Methodological characteristics and forms of WHO target incorporation were recorded separately and could be non-mutually exclusive where a study reported more than one approach or analytical role.

Assessment of methodological characteristics

As part of the methodological characterization of the included studies, information on model calibration, validation, sensitivity analysis, and uncertainty quantification was extracted as reported by the study authors. For calibration, studies were classified according to the reported parameter-fitting approach, including maximum likelihood estimation, Bayesian inference, nonlinear least squares, direct fitting to empirical or baseline data, and the use of previously calibrated parameter sets. A study was classified as performing calibration or parameter fitting when at least one model parameter was estimated or adjusted by fitting model outputs to empirical or baseline epidemiological data; previously calibrated parameter sets were recorded separately. Calibration approaches were treated as non-mutually exclusive when more than one approach was reported.

External validation was recorded when model predictions were compared with independent data not used for calibration, including data from a different setting, population, or time period. Sensitivity analysis was classified as local, global, or structural, with these categories treated as non-mutually exclusive. Uncertainty quantification was recorded when uncertainty in model outputs was characterised using approaches such as Bayesian posterior intervals or stochastic simulations. Sensitivity analysis and uncertainty quantification were recorded separately, allowing studies to be classified under either or both.

Risk of bias and assessment of study quality

In addition to characterising model structures, interventions, and WHO alignment, the methodological quality of the included studies was assessed using the Assessment of Modelling Studies (AMS) tool [31], which is used to evaluate modelling studies in health and economics.

The adapted AMS tool [32] comprised twelve criteria: aims and objectives (A), intervention comparators (C), outcome measures (O), model structure (assessed whether model structure and supporting schematic representation were adequately reported) (S), parameter specification (P), assumptions (As), Data quality, sensitivity, and/or uncertainty assessment (D), model validation (V), results presentation (R), discussion and interpretation (Di), Reporting of funding sources and/or competing interests (CI), and modelling methodology (M). Domain‑specific scores for each criterion are provided in Table 5.

Each criterion was scored on a three-point scale (0 = absent, 1 = partially present, 2 = fully present) [33]. Total scores (maximum 24) were converted to percentages and categorized as low (), medium (), high (), or very high (> 80%).

Bibliometric and network analysis

A bibliometric analysis was conducted using VOSviewer (version 1.6.20) to characterize the research landscape of STH modelling studies. Data were extracted from titles, abstracts, and author affiliations of included studies. Term co-occurrence analysis was used to identify dominant research themes, while co-authorship analysis examined collaboration networks among researchers [34].

A minimum threshold of five occurrences was applied for term inclusion. VOSviewer’s clustering algorithm grouped related terms and authors based on co-occurrence patterns. Network and density visualizations were generated to illustrate thematic structures and colaboration intensity. These analyses complemented the qualitative synthesis by providing insights into research trends, intervention focus areas, and collaborative patterns.

Handling of missing data

During data extraction, several variables were incompletely reported, including predictive timelines, code availability, model validation, calibration, and uncertainty analyses (see S4 File). All data were recorded as reported, and no imputation was performed due to heterogeneity in model structures and outputs. Missing information was explicitly coded as “not reported” and did not constitute grounds for exclusion. These gaps were incorporated into the narrative synthesis as part of the overall assessment of the evidence base.

Trends in the number of published modelling studies

This review analysed 42 mathematical modelling studies published between 2015 and 2024 (Fig 2; Table 1). Four studies (10%) were published in each of 2015, 2016, 2017, 2020, and 2024. Six studies (14%) were published in both 2018 and 2021, while five studies (12%) were published in 2019. Two studies (5%) and three studies (7%) were published in 2022 and 2023, respectively.

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Fig 2. Number of included soil-transmitted helminth (STH) modelling studies by year of publication (2015–2024).

https://doi.org/10.1371/journal.pntd.0013431.g002

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Table 1. Summary of included studies by author, year, transmission unit, modelling framework, population structure, intervention strategy, and timeline.

https://doi.org/10.1371/journal.pntd.0013431.t001

Model taxonomy

The distribution of the 42 included studies across the three pre-specified model-taxonomy dimensions is presented below and summarized in Table 2 and Fig 3.

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Table 2. Summary of model taxonomy across 42 studies. Counts represent number of studies; percentages reflect proportions.

https://doi.org/10.1371/journal.pntd.0013431.t002

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Fig 3. Distribution of model taxonomy characteristics across the 42 included studies, including transmission unit (host- and parasite-based), modelling framework (deterministic and stochastic), and population structure (homogeneous and age-structured).

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Transmission unit

Across the 42 included studies, 13 studies (31%) were classified as host-based models [21–23,37,42,47,50–52,62,63,66,69]. The remaining 29 studies (69%) were classified as parasite-based models [4,12,13,16,35,36,38–41,43–46,48,49,53–61,64,65,67,68].

Mathematical framework

Across the 42 included studies, 26 (62%) were classified as deterministic models [4,21–23,35,37,42–44,46–52,56,58,59,61–64,66,68,69], while 16 (38%) were classified as stochastic models [12,13,16,36,38–41,45,53–55,57,60,65,67].

Population structure

Across the 42 included studies, 14 (33%) were classified as homogeneous (flat) models [21–23,37,42,47–50,52,58,59,63,66], while 28 (67%) were classified as age-structured models [4,12,13,16,35,36,38–41,43–46,51,53–57,60–62,64,65,67–69]. Age structure was represented through either discrete age categories (e.g., pre-school-aged children, school-aged children, and adults) or continuous-age formulations using partial differential or integral equation frameworks.

Pie charts (Fig 3) illustrate the distribution of models across the three taxonomic dimensions, including transmission unit, mathematical framework, and population structure

Intervention decomposition and classification

The distribution of the 42 included studies across the four pre-specified intervention dimensions is presented below and summarised in Table 3.

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Table 3. Distribution of intervention dimensions across 42 modelling studies.

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For intervention strategy, 34 studies (81%) were classified as evaluating preventive chemotherapy (PC), while 8 studies (19%) were classified as evaluating integrated strategies combining PC with one or more complementary interventions, such as WASH, health education, hygiene promotion, or shoe wearing.

For delivery platform, 20 studies (48%) were classified as using combined school- and community-based delivery (SBD + CBD), 16 studies (38%) as using community-based delivery (CBD), and 6 studies (14%) as using school-based delivery (SBD).

For target-population representation, 17 studies (40%) explicitly specified PSAC, SAC, and adults as intervention recipients; 14 studies (33%) applied the intervention to a homogeneous modelled population without explicit demographic stratification of intervention recipients; 4 studies (10%) specified both PSAC and SAC; 3 studies (7%) specified WRA; 2 studies (5%) specified SAC only; and 2 studies (5%) specified SAC and adults. Overall, SAC were explicitly represented among the intervention recipients in 25 studies (60%) across the SAC-containing target-population categories.

For treatment regimen, 40 studies (95%) were classified as evaluating single-drug therapy, while 2 studies (5%) were classified as evaluating dual-drug therapy.

Alignment with WHO targets and reported timelines

Of the 42 included studies, 33 (79%) were classified as aligned with at least one WHO roadmap objective, while 9 (21%) were classified as not aligned. Twelve studies (29%) were classified as explicitly aligned and 21 (50%) as implicitly aligned. Among the explicitly aligned studies, 8 were aligned with the 2011–2020 roadmap and 4 with the 2021–2030 roadmap. Among the implicitly aligned studies, 13 were aligned with the 2011–2020 roadmap and 8 with the 2021–2030 roadmap (Supporting information S4 File).

Among the 12 explicitly aligned studies, 10 operationalised a WHO quantitative programme criterion as an intervention target or input, whereby the criterion specified the intervention level evaluated in the model, while 5 operationalised a WHO quantitative epidemiological threshold as an epidemiological target or endpoint against which modelled epidemiological outcomes were evaluated. These forms of incorporation were not mutually exclusive, as a study could use a WHO programme criterion to define an intervention scenario and also evaluate the resulting epidemiological outcome against a WHO quantitative target.

Among the 21 implicitly aligned studies, 13 evaluated interventions corresponding to the 2011–2020 roadmap objectives without incorporating the WHO quantitative coverage target into the intervention specification or analysis, while 8 evaluated epidemiological outcomes corresponding to the 2021–2030 roadmap objectives without applying the relevant WHO quantitative endpoint or target-attainment criterion.

Among the 42 included studies, 14 (33%) reported a projected timeline for attainment of a WHO-relevant outcome, whereas 28 (67%) did not report a projected timeline (Fig 4; Table 1). Of the 14 studies reporting projected timelines, 7 reported discrete time-to-attainment values (e.g., 2, 5, or 10 years), 6 reported time-to-attainment ranges (e.g., 2–10, 5–6, 3–7, 2–15, and 2–3 years), and 1 reported a projected calendar year (2028) without specifying a relative duration (Table 1).

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Fig 4. Time-bound projections reported by the included modelling studies.

Fourteen studies (33%) reported a time horizon or projected calendar year for a WHO-relevant outcome, whereas 28 studies (67%) did not report a projected timeline.

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Among studies aligned with the 2011–2020 roadmap, 9 reported projected timelines, comprising 5 discrete time-to-attainment values and 4 time-to-attainment ranges. Among studies aligned with the 2021–2030 roadmap, 5 reported projected timelines, comprising 2 discrete time-to-attainment values, 2 time-to-attainment ranges, and 1 projected calendar year (2028).

Factors reported in relation to projected timelines

As part of the post-hoc exploratory analysis, factors reported by study authors in relation to projected timelines were summarised. Among the 14 studies reporting timelines, treatment intensity, including treatment frequency, number of treatment rounds, treatment coverage, or community-wide delivery, was discussed in 11 studies. Drug efficacy was discussed in 5 studies, compliance patterns in 3 studies, and integrated intervention approaches involving preventive chemotherapy combined with WASH-related measures in 3 studies.

Among the remaining 28 studies that did not report projected timelines, reported outcomes included methodological analyses, theoretical investigations, probabilities of elimination, outcomes evaluated at fixed time points, and post-intervention dynamics such as reinfection or rebound patterns.

Bibliometric analysis

A bibliometric analysis was conducted to examine research themes, co-authorship network, and keyword patterns within the included studies [34].

Fig 5 presents a network visualization of frequently co-occurring terms. Three clusters were identified. One cluster included the terms infection, control, treatment, MDA, and preventive chemotherapy. A second cluster included child, school, SAC, and morbidity. A third cluster included community, village, cluster, and elimination. The terms WASH and sanitation were located outside the three principal clusters.

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Fig 5. Network visualization of frequently co-occurring terms.

Red cluster: helminth infections and targeted interventions; Green cluster: children as the primary target population; Blue cluster: study settings (SAC, clusters, communities, villages).

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The co-authorship network (Fig 6) identified three collaboration clusters. The largest cluster comprised Anderson, Truscott, Turner, and Hollingsworth. A second independent cluster included Coffeng, de Vlas, Vegvari, and Hardwick. A smaller cluster connected Werkman and Farrell.

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Fig 6. Co-authorship network derived from the included STH modelling studies.

Nodes represent authors, with larger nodes indicating higher publication frequency. Links represent co-authorship relationships, with thicker links indicating stronger collaboration. Colors denote clusters of closely collaborating authors identified by the network analysis.

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As part of the exploratory analysis, Fig 7 summarizes the helminth species represented in the included modelling studies. Of the 42 studies, 10 articles (24%) modelled hookworm only, 3 studies (7%) modelled Ascaris lumbricoides only, 1 study (2%) modelled Strongyloides stercoralis only, and 1 study (2%) modelled Trichuris trichiura only. Mixed-species models were also identified: 5 studies (12%) included hookworm and Ascaris lumbricoides, 17 studies (41%) included hookworm, Ascaris lumbricoides, and Trichuris trichiura, and 1 study (2%) included hookworm, Ascaris lumbricoides, Trichuris trichiura, and Strongyloides stercoralis. Four studies (10%) considered other helminth or co-infection combinations, including Ancylostoma duodenale with Ostertagia, Ascaris lumbricoides with Schistosoma mansoni, hookworm with lymphatic filariasis, and STH–TB coinfection. Overall, 23 studies (55%) represented more than one helminth species.

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Fig 7. Distribution of helminth species studied across the included modelling articles.

H = hookworm, R = roundworm (Ascaris lumbricoides), W = whipworm (Trichuris trichiura), and S = (Strongyloides stercoralis).

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Methodological characteristics

Across the 42 included studies, methodological characteristics relating to model calibration, validation, sensitivity analysis, and uncertainty quantification were examined. The distribution of these methodological approaches is summarised in Table 4.

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Table 4. Summary of methodological approaches across 42 STH modelling studies.

https://doi.org/10.1371/journal.pntd.0013431.t004

Results on quality assessment of included studies

Quality assessment scores ranged from 70.8% to 95.8% across the 42 included studies. Based on the pre-defined quality categories, 26 studies (62%) were classified as very high quality (>80%), while 16 studies (38%) were classified as high quality (). No studies were classified as medium quality () or low quality ().

The criteria most frequently satisfied across the included studies were clear aims (100%), outcome definition (100%), and modelling methods (100%) (Table 5).

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Table 5. Quality assessment of included studies using the modified Assessment for Modelling Studies (AMS) tool.

https://doi.org/10.1371/journal.pntd.0013431.t005

Recommendations

Based on the synthesis of the 42 included studies, several implications emerge for future model development, reporting, and programme-relevant applications. Given the heterogeneity in model structures, intervention designs, and epidemiological assumptions, these recommendations should be interpreted in relation to the intended research or programme question rather than as universal modelling requirements.

For modelling research, the predominance of parasite-based, age-structured, deterministic, and preventive-chemotherapy-focused models highlights the modelling approaches and intervention questions most frequently represented in the reviewed literature. Alternative structures may provide complementary information where required by the research question. In particular, stochastic approaches may be informative when elimination probabilities, resurgence, or transmission at low prevalence are of interest. The comparatively limited representation of integrated intervention strategies also indicates scope for further evaluation of preventive chemotherapy in combination with complementary measures such as WASH, health education, and hygiene-related interventions.

For models intended to inform programme planning or policy evaluation, WHO-defined quantitative targets or programme criteria may be incorporated according to their intended analytical role, including as intervention scenarios or inputs, epidemiological endpoints, or criteria for assessing target attainment. Where time to a specified programme outcome is an intended model output, projected timelines could be reported together with the epidemiological and intervention assumptions underlying those projections. Appropriate uncertainty quantification and external validation, where independent data are available, may further strengthen the interpretation of model projections for their intended applications.

For programme implementation and policy, greater availability of longitudinal programme data following deworming interventions could facilitate independent evaluation of model predictions and assessment of projected programme outcomes. Such data may strengthen the empirical basis for models intended to evaluate STH control and elimination strategies.

Limitations

This review should be interpreted in light of several methodological considerations. The search was restricted to English-language peer-reviewed articles published between 2015 and 2024 and indexed in Web of Science, Scopus, or Embase. Consequently, relevant studies published before 2015, in other languages, in the grey literature, or indexed exclusively in other databases may have been missed.

Substantial heterogeneity in modelling frameworks, intervention scenarios, outcome measures, and reporting precluded formal meta-analysis; consequently, the findings are based on narrative synthesis. Differences in model structure, assumptions, parameterisation, intervention design, and outcome definitions also limit direct comparison of projections across studies. The review therefore characterises patterns in the modelling literature rather than providing pooled estimates of intervention effectiveness or time to target attainment.

The development and application of the model taxonomy, intervention decomposition framework, and WHO target-alignment classification involved some judgement in assigning studies to predefined categories. Explicit coding rules and reviewer cross-checking were used to promote consistency, but alternative operational definitions may produce different classifications. For WHO alignment specifically, intervention scenario/input and epidemiological endpoint were recorded as distinct analytical roles within explicit alignment and were not interpreted as equivalent uses of a WHO quantitative target or programme criterion.

The review also relied on information reported in the included publications. Incomplete reporting may therefore have resulted in some methodological features being classified as not reported even when they may have been undertaken but not described in the publication. External validation, uncertainty quantification, and projected timelines were reported in only subsets of the included studies; consequently, the review can characterise the extent to which these features were reported but cannot infer their absence where reporting was insufficient or establish the predictive performance or robustness of models for which such assessments were not reported.