A scoping review of transmission models for soil-transmitted helminth infections to underpin the development of a transmission model for Strongyloides stercoralis

Abstract

Soil-transmitted helminth (STH) infections afflict people worldwide, especially in tropical and subtropical regions. Strongyloides stercoralis is distinctive from other STH nematodes by its complex life cycle features of autoinfection, parthenogenesis, and environmental reproduction. This scoping review aims to identify the structures, features, and techniques employed in existing STH models, emphasizing their potential application in describing S. stercoralis infection dynamics. A comprehensive search was conducted in the Medline, Embase, and Scopus databases for studies published until 14 June 2024. A total of 47 studies presenting a new model or novel adaptation of an existing model to human STH infection transmission were identified: only one described S. stercoralis transmission in humans. The identified models were predominantly deterministic and focused on the dynamics of mean worm load within hosts and the infectiousness of the environmental reservoir. One model addressed transmission in multi-host scenarios, as not all STH transmission cycles involve multiple hosts. Models were frequently used to simulate the effectiveness of mass drug administration, including drug efficacy and treatment coverage, while water, sanitation, and hygiene (WASH), health education, and vaccination were less explored. Given the limitation of individual-level data, compartmental models may be a reasonable starting point for S. stercoralis transmission. For a comprehensive understanding, incorporating parasite life cycle features into the model, exploring multi-host dynamics, including a diverse range of host heterogeneities, and assessing the impact of climatic factors like rainfall and land surface temperature on parasite survival in the environment may be beneficial, especially in settings where their importance is notable.

Introduction

Soil-transmitted helminth (STH) infections afflict people worldwide, particularly those living in tropical and subtropical regions and rural areas of Sub-Saharan Africa, Latin America, China and South and Southeast Asia (Brooker et al., 2006; Pullan et al., 2014). The term STH encompasses a group of parasitic nematodes, including roundworm (Ascaris lumbricoides), whipworm (Trichuris trichiura), hookworms (Necator americanus, Ancylostoma ceylanicum and Ancylostoma duodenale) and Strongyloides stercoralis (Colella et al., 2021; World Health Organization, 2023). STHs are primarily transmitted through skin penetration of infective larvae or ingestion of eggs present in soil contaminated with human or animal faeces (Mbong Ngwese et al., 2020). In 2010, it was estimated that 1.45 billion individuals were infected with STHs, resulting in an estimated 4.98 million years lived with disability (YLDs) and 5.18 million disability-adjusted life years (DALYs) globally (Pullan et al., 2014).

Strongyloides stercoralis is distinctive from other STH nematodes due to its complex life cycle features of auto-infection, parthenogenesis and environmental reproduction (Page et al., 2018). Some genotyping studies (Jaleta et al., 2017; Nagayasu et al., 2017) have shown the presence of 2 distinct populations of S. stercoralis genotypes – one shared between dogs and humans and the other exclusive to dogs. Due to parthenogenesis and autoinfection, S. stercoralis infection can lead to prolonged and potentially fatal hyper infection or disseminated strongyloidiasis in infected hosts (Greiner et al., 2008; Toledo et al., 2015; Page et al., 2018). In 2013, it was estimated that at least 370 million individuals were infected with S. stercoralis, comparing the prevalence of hookworm infection and the sensitivity of diagnostic techniques for both hookworms and S. stercoralis (Bisoffi et al., 2013). However, a review study in 2017 estimated that over 600 million people were infected with S. stercoralis based on prevalence data collected from endemic countries worldwide between 1990 and 2016 (Buonfrate et al., 2020). Although S. stercoralis infection is endemic to rural areas of tropical and subtropical countries, it has also been identified in temperate regions of high-income countries, such as Australia, Japan, Spain, Italy and the United States (Krolewiecki and Nutman, 2019). Various factors are associated with the risk of this infection, including behaviour, socio-demographics, environment and historical infection exposure (Adams et al., 2003; Steinmann et al., 2007; Khieu et al., 2013; Fleitas et al., 2022). S. fuelleborni subsp. fuelleborni is a parasitic nematode of non-human primates that can rarely infect humans (Nutman, 2017; Al-Jawabreh et al., 2024). Further research is needed to clarify the distribution range of other Strongyloides species and the extent to which they can infect humans.

STH transmission models are primarily used to analyse the complex interplay between environmental reservoirs and hosts to understand how worm burdens and/or infection prevalence change over time. These models offer a comprehensive insight into STH transmission dynamics and are useful for forecasting trends of infection dynamics, evaluating preventive interventions and informing control programs. Components of published STH transmission models may be adapted to simulate the transmission dynamics of S. stercoralis, which, like other STHs, is spread through an environmental reservoir and shares some commonalities in the life cycle. Hence, this review aims to analyse published STH models to develop a new model for S. stercoralis transmission. Using narrative synthesis, the review identified the structures, features and techniques employed in STH models, emphasising their potential application in describing S. stercoralis infection dynamics. Key aspects explored include modelling the parasite's life cycle, integrating the environmental reservoir and within-host dynamics into the model, addressing host heterogeneities, including multi-host scenarios where applicable, evaluating preventive interventions and informing the choice of modelling individual worm burden or prevalence in individuals infected with S. stercoralis.

Materials and methods

This scoping review was reported according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for scoping reviews (PRISMA-ScR) guidelines and checklist (Tricco et al., 2018) (Supplementary Data S1).

Search strategy

A comprehensive search was conducted on 14 June 2024, in the Medline, Embase and Scopus databases for studies published until 14 June 2024. The databases were searched using 2 categories of keywords, one for STH and the other for modelling, as follows:

• • STH: sth OR helminthiasis OR helminth* OR hookworm* OR roundworm* OR whipworm* OR threadworm* OR Trichuris trichiura OR Necator americanus OR Ancylostoma ceylanicum OR Ancylostoma duodenale OR Ascaris lumbricoides OR Ascaris suum OR Strongyloides stercoralis OR ancylostomiasis OR necatoriasis OR ascariasis OR strongyloidiasis OR trichuriasis

  AND

• • Modelling: mathematical model OR epidemiological model OR simulat* OR agent-based OR individual-based OR differential equation OR age-structured OR transmission model OR deterministic OR stochastic.

Medical Subject Heading (MeSH) and Embase Subject Heading (Emtree) terms were used in Medline and Embase, respectively.

Eligibility criteria

Original peer-reviewed articles with full text available in English, presenting a modelling approach to describe the transmission dynamics of STH infections in humans, were considered eligible. Protocols, systematic or literature reviews, conference abstracts, statistical models, in vitro models, models that focus solely on animal infections and follow-up articles based on previously reported models that did not introduce novel modelling mechanisms were excluded. There were no restrictions on geographical areas, and the date of publication was up to 14 June 2024.

Study selection

Two authors (PTC, MW) independently screened the title and abstract of the retrieved papers in Covidence (Veritas Health Innovation, 2023), with differences resolved through discussion between the authors. Records that met the eligibility criteria and those that required further assessment underwent full-text screening by a single author (MW) to ensure alignment with the scope and objectives of the review. The final selection of articles was determined through discussion and consensus among all authors before data extraction.

Data extraction

An extraction tool was prepared in Microsoft Excel (version 16.75.2) to extract the following data: Study information (title, publication year, first author), study aims, considered parasites, model framework, hosts and host heterogeneities, environmental reservoir and seasonality, intervention strategies, key functions used to describe the transmission dynamics and study limitations.

Synthesis of results

The selected studies were grouped based on several key aspects: model framework and approaches, host heterogeneities, environmental reservoir, within-host dynamics, key transmission functions and interventions. Within each group, common techniques were identified, and the differences in techniques across the studies were assessed.

As the focus of this review was to identify STH transmission model features and their potential applicability to S. stercoralis, a formal critical appraisal of the methodological quality of individual studies was not conducted.

Results

A total of 1309 articles was identified – 490 from Medline, 524 from Embase and 295 from Scopus. After deduplication, screening and full-text review, 47 papers were selected for data extraction. A PRISMA flow diagram (Fig. 1) summarizes the stages of the selection process.

Figure 1. PRISMA flow diagram.

Characteristics of included studies

Table 1 presents the modelling studies in chronological order. This arrangement provides a structured overview that captures the modelling framework (compartmental or individual-based), the underlying model mechanics (deterministic or stochastic), whether the model builds upon a previous modelling effort included in this review, and the specific parasite(s) subject of investigation.

Table 1. Framework, approach, links to previous models, and parasites of included studies

^a The model was derived from this referenced model and expanded upon by incorporating the age heterogeneities of hosts.

^b The referenced model served as the basis for describing heterogeneity in infection rates among hosts.

^c The age structure of the model was built upon the framework provided by this referenced model.

^d The analysis of data and assessment of the effects of various preventive strategies were conducted using this referenced model.

^e The referenced model expanded by including multiple helminth infections, integrating treatment with diverse medicines, and evaluating the costs, disability, and cost-effectiveness of a mass drug administration program.

^f The referenced deterministic model was used to obtain epidemiological parameters from individual level data.

^g This referenced model was expanded to evaluate the impacts of WASH interventions.

^h This referenced model was used to perform a sensitivity analysis.

ⁱ The referenced model was used to develop a model for studying parasite transmission and the effects of MDA.

^j The referenced model was adapted to develop an individual-based stochastic model for simulating STH transmission and treatment.

Deterministic approach

The majority of models employed a deterministic compartmental framework. Specifically, numerous models (Anderson and May, 1982, 1985b; Bundy et al., 1985; Medley et al., 1993; Chan et al., 1994, 1997; Alexander et al., 2011; Anderson et al., 2013, 2017; Truscott et al., 2014a, 2014b, 2015; Lo et al., 2015; Turner et al., 2015, 2016a, 2016b; Davis et al., 2018; Farrell and Anderson, 2018; Hardwick et al., 2020; Chong et al., 2021, 2022; Okoyo et al., 2021; Walker et al., 2023) were based on the deterministic helminth model proposed by Anderson and Anderson and May (Anderson, 1980, 1982; Anderson and May, 1985a, 1991) – a modelling framework that represents the parasite life cycle through 2 compartments: mature worms within the host and infective stages (eggs or larvae) in the environment. Essentially, Anderson's and Anderson & May's (Anderson, 1980, 1982; Anderson and May, 1985a, 1991) models employed 2 differential equations to portray the rate of change in mean worm burden within the host and per capita infectiousness of the environmental reservoir.

Several models based on Anderson's and Anderson & May's framework were enhanced by introducing novel elements: Medley et al. (1993) introduced a susceptibility factor to measure a host's relative susceptibility to parasite establishment, Chan et al. (1994) incorporated age structure to study different worm burdens within various age groups, Chong et al. (2021) introduced an impulsive mean worm model and its modified version to examine instantaneous changes in mean worm burdens in hosts immediately before and after Mass Drug Administration (MDA), Chong et al. (2022) developed a prevalence-based deterministic model to analyse STH transmission dynamics, focusing on prevalence rather than worm burdens, Davis et al. (2018) included several stages of A. lumbricoides worm development in their model, and Walker et al. (2023) developed a multi-host transmission model that includes humans and dogs.

Churcher et al. (2005) developed a deterministic, individual-based model estimating the number of eggs contributed by an individual host (effective transmission contribution) based on a predetermined worm burden. The model considered positive and negative density-dependent processes (Keeling and Rohani, 2011) within the parasite's life cycle. Furthermore, the authors highlighted the importance of understanding individual-level variations in worm burden and emphasized that failure to capture them may result in inaccurate estimates of transmission.

Several SEIR – susceptible, exposed, infectious and resistant (or recovered) – deterministic compartmental models have been employed to describe the transmission dynamics of parasitic infections in humans, considering various life stages of the parasite within the human and the environment. Three studies (Bartsch et al., 2016; Pawelek et al., 2016; Lambura et al., 2020) utilized the SEIR model structure to depict the transmission of infection among human hosts. Two studies (Bartsch et al., 2016; Pawelek et al., 2016) incorporated larval developmental stages in the environment through mutually exclusive compartments. In Bartsch et al. (2016), the parasite population in the environment was divided into 2 compartments: 1 for dormant eggs and non-infectious larvae and another for infectious larvae. Pawelek et al. (2016) delineated 3 distinct stages: eggs in faeces, second-stage non-infective larvae and third-stage infective larvae compartments. In contrast, the third of these SEIR models (Lambura et al., 2020) represented the parasite populations in the environment as a single compartment. Oguntolu et al. (2024) introduced a hygiene conscious (H) compartment in addition to the SEIR host compartments into their model to study the impact of hygiene awareness on infection transmission in the human population. Details of the host and parasite compartments used in the deterministic models are presented in Table 2.

Table 2. Compartments used in deterministic compartmental models

Stochastic approach

A subset of models (Medley et al., 1993, 2016; Galvani, 2003; Walker et al., 2010; Alexander et al., 2011; Wang et al., 2012; Truscott et al., 2014a, 2017, 2019, 2021; Coffeng et al., 2015; Anderson et al., 2017; Farrell et al., 2017, 2018; Coffeng et al., 2018; Werkman et al., 2018, 2020; Vegvari et al., 2019; Hardwick et al., 2020, 2021; Malizia et al., 2021; Borlase et al., 2022; Collyer and Anderson, 2024) adopted a stochastic framework. Almost all of these models employed an individual-based modelling approach that accounted for worm aggregation within the individuals, individual-level heterogeneity and tracking of individual behaviours that influence infection exposure and treatment compliance. To accommodate worm aggregation within hosts, these models depart from the assumption of uniform worm distribution by incorporating a negative binomial distribution. With this approach, it was assumed that most hosts carry a low number of worms while a small fraction carries high burdens.

The only model dedicated to S. stercoralis transmission, developed by Collyer and Anderson (2024), is a stochastic individual-based model that only considers human hosts. The model examined individual host behaviours and described the interactions between worm burdens within the host and larvae in the environment, capturing the randomness of infection acquisition, autoinfection, worm death and larvae maturity.

Four models (Anderson et al., 2017; Werkman et al., 2018; Vegvari et al., 2019; Hardwick et al., 2021) utilized the individual-based stochastic model described in Truscott et al. (2016) review paper, which focuses on modelling individual worms within hosts rather than transmission dynamics within the human population. Two of these models (Vegvari et al., 2019; Hardwick et al., 2021) expanded upon the model by integrating age structure and migration patterns into their modelling approaches.

Another 5 models (Coffeng et al., 2015, 2018; Farrell et al., 2018; Malizia et al., 2021; Borlase et al., 2022) employed the WORMSIM model framework (Coffeng et al., 2015), an individual-based modelling framework that facilitates the study of transmission and control of helminth infections by accounting for various individual-level heterogeneities. By design, WORMSIM calculates the infection transmission dynamics of individuals and within-host parasites stochastically, while the dynamics of infective material in the environment are simulated deterministically.

One model (Walker et al., 2010) employed a stochastic immigration-death process to study the acquisition of infections from the environment. This model incorporated 3 compartments of life stages of worm development within the host: pre-intestinal within-tissue migrating larval worms, ‘small’ adult worms and ‘large’ adults that develop from the small ones.

Anderson et al. (2017) utilized Anderson (1980)'s and Anderson and May (1982); Anderson and May (1985b) 's deterministic framework to predict the required MDA coverage for treating different age groups to control transmission and an individual-based stochastic framework (Truscott et al., 2016) to calculate the positive and negative predictive values for a defined prevalence of infection 2 years after the cessation of MDA. Similarly, many models (Medley et al., 1993; Wang et al., 2012; Hardwick et al., 2020) used Anderson and May's (Anderson and May, 1991) deterministic framework and extended the analysis by developing a stochastic model. Alexander et al. (2011) ranked the statistical power of 3 efficacy measures and used a modelling approach to estimate the likely impact of trial interventions on the force of infection.

Host heterogeneities

The review identified several host heterogeneities that significantly influence infection transmission, including age, sex, immunity level and personal factors such as behaviour and occupation. Most models (Chan et al., 1994, 1997; Anderson et al., 2013, 2017; Truscott et al., 2014a, 2014b, 2015, 2017, 2019, 2021; Coffeng et al., 2015, 2018; Lo et al., 2015; Turner et al., 2015, 2016a, 2016b; Bartsch et al., 2016; Medley et al., 2016; Farrell et al., 2017, 2018; Farrell and Anderson, 2018; Werkman et al., 2018, 2020; Vegvari et al., 2019; Hardwick et al., 2021; Malizia et al., 2021; Okoyo et al., 2021, 2022) have incorporated age heterogeneity to account for variations in infection transmission across different age groups: pre-school aged children, school-aged children, women of childbearing age and adults. This categorization was primarily influenced by the World Health Organization's (WHO) objective of administering routine preventive chemotherapy to at least 75% of pre-school-aged children and school-aged children for STH control by 2020 (Truscott et al., 2016).

Individual-based frameworks, exemplified by the WORMSIM modelling framework (Coffeng et al., 2015, 2018), significantly contributed to understanding host-pathogen interactions by accommodating various forms of host heterogeneity. In WORMSIM, an individual's contribution to the environmental reservoir and acquisition of infection were considered to be influenced by age, sex and personal factors such as behaviour and occupation. Some studies stratified human hosts based on their immunological responsiveness (Anderson and May, 1985b; Galvani, 2003) and susceptibility factor (Medley et al., 1993; Wang et al., 2012). In Walker et al. (2010), adult worm mortality and growth rates in the host were defined as random variables to incorporate heterogeneities among hosts. In Farrell et al. (2017) model, individuals were assigned to a personal predisposition index to account for differential exposure to infection due to a range of possible host genetic, immunological, behavioural, social or environmental factors. Collyer and Anderson (2024)'s model included age-dependent worm acquisition from the environment, which, combined with the negative binomial distribution of new infections from the environment, resulted in heterogeneous worm burdens within the hosts.

Only one study (Walker et al., 2023) developed a model capable of capturing the host-species heterogeneity. Walker et al. (2023) incorporated both human and non-human hosts into their model and studied the interaction between different host species and the environmental reservoir. This extension sheds light on the interplay between human and animal hosts and offers a reliable framework for studying multi-host infection dynamics.

Environmental reservoir dynamics

In considering the environmental reservoir, the per capita infectiousness of the shared reservoir was a key consideration, influenced by the host's contribution to the reservoir, acquisition of infection and mortality of infective larvae in the environmental reservoir. Only a few models (Galvani, 2003; Bartsch et al., 2016; Pawelek et al., 2016; Davis et al., 2018; Collyer and Anderson, 2024) have incorporated the developmental stages of larvae in the environment. The Collyer and Anderson (2024) model incorporated significant life stages of S. stercoralis in the environment: first- and second-generation larvae and mature worms. The model encompassed the environmental reproduction of S. stercoralis and different mortality rates among its life stages. This helps capture the parasite's persistence and worm burden in the environment, and their impact on S. stercoralis transmission.

In many models, the environmental reservoir was considered to be common to all age groups. To address the aspects of environmental contamination, the fecundity of worms within hosts, with or without the effect of density dependence, has been considered. Moreover, models with different host characteristics have hypothesized differences in environmental contamination and infection acquisition according to host heterogeneity.

Figure 2 summarizes the factors that influence environmental dynamics, such as carrying capacity, seasonal effects and migration patterns.

Figure 2. Key factors influencing environmental reservoir dynamics.

Within-host dynamics

In deterministic modelling frameworks, the primary focus was often on assessing the mean parasite burden within the hosts (Anderson and May, 1982, 1985b; Bundy et al., 1985; Medley et al., 1993; Chan et al., 1994, 1997; Alexander et al., 2011; Wang et al., 2012; Anderson et al., 2013; Truscott et al., 2014a, 2014b, 2015; Lo et al., 2015; Turner et al., 2015, 2016a, 2016b; Davis et al., 2018; Hardwick et al., 2020; Chong et al., 2021, 2022; Okoyo et al., 2021, 2022; Walker et al., 2023). This evaluation involved examining factors such as the strength of contact with the reservoir and the mortality rates of the hosts and worms within the host, which describes how the mean worm burden in the population changes over time.

To account for within-host dynamics, Collyer and Anderson (2024) incorporated the unique life cycle features of S. stercoralis, including autoinfection and reproduction dynamics, into their model. The model also simulated larvae migration from the environment, larvae maturation within the host, larvae excretion into the environment and larvae death within the host. The excretion of first-generation larvae into the environment was assumed to be proportional to the egg production within the host. Furthermore, Collyer and Anderson (2024) defined the basic reproduction number in their model as the sum of 2 terms: the basic reproduction number for free life cycle and the basic reproduction number for within host autoinfection. This approach successfully accounted for separate dynamics related to inter host and intra host S. stercoralis transmission.

Numerous models have integrated density-dependent fecundity of worms within hosts into their models (Anderson and May, 1982; Bundy et al., 1985; Medley et al., 1993, 2016; Chan et al., 1994, 1997; Galvani, 2003; Churcher et al., 2005; Alexander et al., 2011; Wang et al., 2012; Anderson et al., 2013, 2017; Truscott et al., 2014a, 2014b, 2015, 2019, 2021; Coffeng et al., 2015; Lo et al., 2015; Turner et al., 2015, 2016a, 2016b; Bartsch et al., 2016; Farrell et al., 2017; Coffeng et al., 2018; Davis et al., 2018; Farrell and Anderson, 2018; Werkman et al., 2018, 2020; Vegvari et al., 2019; Hardwick et al., 2020, 2021; Chong et al., 2021, 2022; Okoyo et al., 2021, 2022; Walker et al., 2023; Collyer and Anderson, 2024). This density-dependent fecundity captured how worm density within hosts affects their reproductive capacity and reflects the constraints imposed by the limited resources available to the worm population within the host. Additionally, the mating probability factor was incorporated to account for the impact of sexual reproduction (Bundy et al., 1985; Churcher et al., 2005; Truscott et al., 2014a, 2014b, 2015, 2019, 2021; Coffeng et al., 2015, 2018; Vegvari et al., 2019; Hardwick et al., 2020; Werkman et al., 2020; Chong et al., 2021, 2022; Malizia et al., 2021; Okoyo et al., 2021, 2022; Walker et al., 2023).

The WORMSIM model framework takes a more comprehensive approach by incorporating factors such as the lifespan of worms within the host, age-dependent reproductive capacity, the longevity of infective material within the host, mating cycle, male potential and female worm fecundity (Coffeng et al., 2015). This detailed representation aims to provide a more accurate depiction of transmission dynamics. In some models (Bundy et al., 1985; Walker et al., 2010; Bartsch et al., 2016; Davis et al., 2018) worm maturation within the host was incorporated into the model.

In most cases (Bundy et al., 1985; Churcher et al., 2005; Walker et al., 2010; Wang et al., 2012; Anderson et al., 2013; Truscott et al., 2014b, 2015, 2019, 2021; Coffeng et al., 2015; Turner et al., 2015, 2016a, 2016b; Bartsch et al., 2016; Medley et al., 2016; Farrell et al., 2017; Davis et al., 2018; Werkman et al., 2018, 2020; Hardwick et al., 2020; Walker et al., 2023), the worm burden is divided by the sex of the worms, representing a proportion of the total female worms in the host. Only a few studies (Anderson and May, 1985b; Medley et al., 1993; Galvani, 2003; Coffeng et al., 2015, 2018; Farrell et al., 2017) focused on the effect of host immunity on incoming infection and worm aggregation within the host.

Key functions describing transmission dynamics

Some dominant parameters in STH transmission models are expressed using functional forms to depict the dynamics of transmission. The force of infection, a pivotal determinant of infection transmission dynamics, describes the rate at which hosts acquire infections through interactions with the environmental reservoir. In Walker et al. (2010), the force of infection is defined as the average rate that hosts acquire the adult worm. In the WORMSIM framework (Coffeng et al., 2015, 2018), the force of infection operates at both the population and individual levels. The population level force of infection depends on the infective material in the environment, overall exposure rate and the probability of successful infection. The individual force of infection is then a product of the population-level force of infection and individual exposure, and this individual exposure is dependent on age, sex and personal factors. Truscott et al. (2021), defined the force of infection for the acquisition of female worms as the product of individual strength of contact with the infectious reservoir, age-dependent contact rate and quantity of infectious material in the environmental reservoir.

Several models consider density-dependent transmission, where infection transmission depends on the density of eggs or larvae. Some models deviate from the density-dependent transmission by assuming that the population of infectious eggs or larvae in the environment is constant or at equilibrium (Walker et al., 2010, 2023), or by considering transmission independent of host population size (Truscott et al., 2021). However, several models (Chan et al., 1994, 1997; Hardwick et al., 2020; Chong et al., 2021, 2022) considered density-dependent transmission and then assumed the infective material in the environmental reservoir is at equilibrium for the model simulations.

For parasite reproduction, several models utilized mean egg output and mating probability of adult worms, as described by Anderson and May (1991). These parameters depend on the mean number of worms in a human population, the clumping parameter of the negative binomial distribution and density-dependent coefficient within the host. Churcher et al. (2005) expressed density-dependent net fecundity as a function of the number of female worms within a host, the maximum egg output per adult female worm and a measure of the severity of density-dependent fecundity. This density-dependent fecundity expression involves the exponential of the negative product of density-dependent fecundity severity measure and a number of adult female worms, indicating that as the number of adult female worms increases, fecundity experiences a rapid rise but may eventually approach a saturation point or maximum level. In WORMSIM, the reproduction capacity of a female worm is described as a product of the potential reproductive capacity of a female worm after patency, the mating factor and the exponential fecundity coefficient.

The relationship between the prevalence of infection and mean worm burden within hosts is often described by assuming a negative binomial distribution of worms per host. The functional forms used in the models to describe the force of infection, parasite reproduction and the prevalence of infection are summarized in Supplementary Table 1.

Interventions

In modelling infection control, various interventions such as MDA, WASH (i.e. the ability to access water, sanitation and hygiene), health education initiatives and hypothetical vaccine interventions were considered.

The majority of the models focused on assessing the effectiveness of MDA programs in controlling STH infections within the communities (Anderson and May, 1982, 1985b; Bundy et al., 1985; Medley et al., 1993, 2016; Chan et al., 1994, 1997; Walker et al., 2010; Wang et al., 2012; Anderson et al., 2013, 2017; Truscott et al., 2014a, 2014b, 2015, 2017, 2021; Coffeng et al., 2015; Lo et al., 2015; Turner et al., 2015, 2016a, 2016b; Bartsch et al., 2016; Pawelek et al., 2016; Farrell et al., 2017, 2018; Coffeng et al., 2018; Davis et al., 2018; Farrell and Anderson, 2018; Werkman et al., 2018, 2020; Vegvari et al., 2019; Hardwick et al., 2020, 2021; Lambura et al., 2020; Chong et al., 2021; Malizia et al., 2021; Okoyo et al., 2021, 2022; Borlase et al., 2022; Walker et al., 2023; Collyer and Anderson, 2024). These models primarily evaluated the effectiveness of WHO-recommended preventive chemotherapy strategies (World Health Organization, 2013; World Health Organization, 2017). The predicted impact of several WHO-recommended drugs, including mebendazole, albendazole, ivermectin and pyrantel pamoate, was evaluated using models for different parasites, incorporating variations in efficacy, treatment frequencies and coverage levels across host strata. Furthermore, to quantify the effectiveness of MDA programs, diverse mechanisms of action were taken into account in the models: the effect of treatment on the effective reproduction number (Bundy et al., 1985; Anderson et al., 2013; Truscott et al., 2014a), reduction in mean worm burden or eggs and reduction of prevalence (Anderson and May, 1985b; Medley et al., 1993, 2016; Chan et al., 1994; Walker et al., 2010; Truscott et al., 2014b, 2015; Coffeng et al., 2015, 2018; Lo et al., 2015; Turner et al., 2015, 2016a; Bartsch et al., 2016; Pawelek et al., 2016; Farrell et al., 2017; Davis et al., 2018; Werkman et al., 2018, 2020; Vegvari et al., 2019; Chong et al., 2021; Hardwick et al., 2021; Okoyo et al., 2021; Collyer and Anderson, 2024). One study (Turner et al., 2016b) used the total number of worm years averted, number of years with infection and number of years with heavy infection as effectiveness metrics.

Few models incorporated WASH interventions as an STH control strategy (Coffeng et al., 2015, 2018; Lambura et al., 2020; Okoyo et al., 2021, 2022). Models explored different WASH modalities (e.g. none, sanitation only and hygiene only) in their capacity to modify the infectiousness of the environmental reservoir, the force of infection and changes in host contribution to the environmental reservoir. The combined impact of MDA and WASH interventions on the worm burden and the time required to interrupt STH transmission were also assessed (Coffeng et al., 2015, 2018; Lambura et al., 2020; Okoyo et al., 2021, 2022). In one model (Coffeng et al., 2015), the potential effects of health education and WASH were assumed to reduce the host's contribution to the infective material in the environmental reservoir by 50%, with equality for all hosts. Oguntolu et al. (2024) investigated the influence of hygiene consciousness within susceptible and infectious compartments on infection transmission.

Only 2 models (Coffeng et al., 2015; Lambura et al., 2020) incorporated the effectiveness of health education as a control measure for STH infections. In Lambura et al. (2020), the effectiveness measure of health education was incorporated into the force of infection, with a value of 0 indicating ineffectiveness, while a value of 1 represented complete effectiveness. Notably, Lambura et al. (2020) was the only study that considered all 3 preventive strategies: MDA, WASH and health education, by incorporating 3 time-dependent parameters into the model.

Walker et al. (2023) considered a human-only and One Health (humans and dogs) MDA strategy. They simulated different treatment scenarios for humans, including annual and biannual treatments for endemic prevalence levels of humans ≥20% and ≥50%, respectively, with 75% coverage using albendazole. Additionally, they assumed that the dogs were treated with a spot-on anthelminthic using moxidectin, with coverage ranging from 25 to 75%.

It is worth noting that while the development of vaccination for STH infections is still an ongoing process (Zawawi and Else, 2020) and no STH vaccination is in place, some studies considered the hypothetical efficacy of vaccination as a control measure, using an arbitrary efficacy rate (Anderson and May, 1982; Alexander et al., 2011; Bartsch et al., 2016). Bartsch et al. (2016) modelled the vaccine to reduce the likelihood that invading L3 larvae develop into mature adults and to increase the likelihood of eliminating a proportion of mature worms present at vaccination, and Alexander et al. (2011) conducted an investigation to assess the statistical power of the vaccine trial interventions and their impact on reducing the force of infection. Furthermore, Anderson and May (1982) examined the proportion of the population that must be immunized with a reliable vaccine to reduce the effective reproductive number below unity. The intervention strategies and outcome measures considered in the studies are summarized in Fig. 3.

Figure 3. Preventive interventions and effectiveness measures.

Discussion

In this scoping review, the primary objective was to evaluate various models employed to understand the transmission dynamics of STH in order to identify techniques applicable to modelling S. stercoralis infection. At the time of the search, only one model describing the dynamics of S. stercoralis infection, focusing exclusively on humans, was identified. Researchers utilized deterministic and stochastic approaches, employing compartmental and individual-based frameworks to capture the complexity of STH transmission dynamics. Host heterogeneities, including age, sex and immunity, were often included in models. Insights into the environmental reservoir may require refinement to consider the specificities of S. stercoralis life stages, climatic factors on parasite survival in the environment, and the role of parasite reproduction in the environment. Understanding within-host dynamics, particularly the challenges posed by autoinfection, remains an essential focus. While interventions such as MDA, WASH, health education and vaccination were assessed using models, there is an opportunity for future modelling work to focus on a comprehensive One Health approach to reduce S. stercoralis transmission.

In this review, a burgeoning global interest in exploring STH transmission dynamics was identified. In the 1990s, only a few research groups delved into this area, but the review highlights a remarkable contemporary shift in research focus. This shift can be attributed to several factors, including heightened awareness of the global burden of STH infections, advances in modelling techniques, improved data availability and the acknowledgment of STH as a significant public health issue, as outlined in the WHO Roadmap for Neglected Tropical Diseases (World Health Organization, 2022).

Most models relied on a deterministic approach, possibly influenced by factors such as simplicity, the consistency of outcomes and computational efficiency. However, deterministic models may not fully capture the complexities of STH infection transmission as they overlook inherent randomness in biological processes, including worm acquisition, worm reproduction, egg or larvae deposition and parasite death. On the other hand, stochastic models offer a more realistic representation of the complexities observed in real-world infection transmission scenarios and are well suited for capturing randomness in biological processes. This approach allows for running multiple simulations capturing many possible futures, enabling the analysis of the distribution of possible outcomes and the estimation of probabilities.

The choice of the framework to describe the transmission dynamics of S. stercoralis infection should align with the research objectives, considerations and data availability. Compartmental models, describing average behaviour in homogeneous compartments (host/parasite), prove valuable for certain investigations. Individual-based models are particularly suitable for studying transmission dynamics within individuals, especially in scenarios with low prevalence or with important host heterogeneities. Due to the limitations of individual-level data and to reduce the complexities associated with the inherent randomness in the biology of S. stercoralis, deterministic compartmental models may serve as a reasonable starting point for modelling S. stercoralis transmission.

The prevalence of S. stercoralis is impacted by age, sex and various behavioural factors, exhibiting distinct patterns compared to other STH nematodes (Khieu et al., 2014). One of the main findings in this review is that less attention has been given to incorporating host heterogeneities into STH models. The majority of models focused on age disparities in their model simulations, often with a primary focus on child-targeted prevention programs. However, Coffeng et al. (2018) considered the importance of incorporating host diversities such as age, sex and personal factors into the model in controlling the infection.

Moreover, understanding the role of multiple hosts in pathogen transmission may be important to capture S. stercoralis transmission dynamics and the impact of control strategies. Walker et al. (2023) supported this by incorporating humans and dogs into the A. ceylanicum transmission model and highlighting the importance of One Health interventions. Collyer and Anderson (2024) examined S. stercoralis infection transmission solely in humans while acknowledging uncertainties regarding the involvement of dogs as hosts in S. stercoralis transmission. However, several studies have found S. stercoralis cross infection between humans and dogs (Bradbury and Streit, 2024) and the existence of a lineage of S. stercoralis that can infect humans and dogs (Jaleta et al., 2017; Nagayasu et al., 2017). Hence, dogs' contribution to the reservoir and their acquisition of S. stercoralis can influence the infection dynamics of the environmental reservoir and, subsequently, the dynamics of S. stercoralis transmission in humans. Moreover, the behaviour of dogs, including roaming patterns and defecation, might influence the spatial distribution of larvae in the environment, thereby affecting the risk of human exposure. A model incorporating both hosts, humans and dogs, would allow exploration of the contribution of dogs to the human burden of strongyloidiasis by capturing the interconnection between hosts that occurs via the environment. A greater understanding of these transmission processes could facilitate the design of an effective control strategy to reduce the overall burden of infection.

In modelling the environmental reservoir – a factor that plays a significant role in the STH parasite life cycle dynamics – most models have considered the contribution of hosts to the environmental reservoir, the acquisition of infective material from the reservoir and the survival of infective material in the environment. However, there has been a tendency to overlook the seasonal effects on the environmental reservoir (only included in Davis et al. (2018)) and the carrying capacity of larvae or eggs in the environment (Lambura et al., 2020; Oguntolu et al., 2024). S. stercoralis exhibits unique features in its free-living cycle, involving parasite reproduction in the environment and the short life expectancy of infective larvae, distinguishing it from other STHs. The Collyer and Anderson (2024) model comprehensively captured these S. stercoralis life cycle stages and underscored their importance of considering parasite's life cycle in modelling to understanding transmission dynamics. Furthermore, modelling of S. stercoralis may requires special attention to the environmental risk factors such as annual rainfall, land surface temperature and land coverage (Forrer et al., 2019).

Within-host dynamics were frequently focused on mean worm loads, larvae maturation and reproduction within the host. Parameters influencing transmission between the host and the reservoir and the life span of the worm in the host contributed to describing the mean worm burden. Additionally, incorporating fecundity and mating probability into the model addressed parasite reproduction within the host in some of the reviewed STH models. In modelling S. stercoralis within host dynamics, Collyer and Anderson (2024) incorporated S. stercoralis life cycle features, including autoinfection and within-host reproduction, and successfully captured the resulting worm burdens within the host. This also exemplified the importance of life cycle features on transmission dynamics.

Interventions, mainly MDA, were extensively modelled for human populations. Since S. stercoralis epidemiology is interrelated with humans, dogs and the environment (Page et al., 2018; Bradbury and Streit, 2024), achieving optimal outcomes may necessitate interventions that target infection control across these 3 sectors. Designing interventions to control the parasite population in the environment directly may be less critical due to S. stercoralis' free-living cycle being limited to a single, short-lived and generation (Page et al., 2018). However, it remains crucial to manage parasite shedding from hosts into the environment and reduce host exposure to infective larvae, as this is the primary route of S. stercoralis transmission for humans and dogs. While the potential role of dogs in transmitting S. stercoralis remains uncertain, experimental studies have shown that S. stercoralis can infect both humans and dogs (Bradbury and Streit, 2024). Moreover, several genotyping studies have identified different genotypes of S. stercoralis, with one lineage capable of causing infections in both species and another exclusively in dogs (Jaleta et al., 2017; Nagayasu et al., 2017). Future population genomic studies will help elucidate the transmission dynamics of S. stercoralis between dogs and humans. Hence, models may be used to demonstrate whether dogs play a significant role in S. stercoralis transmission through environmental contamination, acquisition and the spread of infections. If this the case, considering dogs in intervention strategies may provide an additional avenue to control S. stercoralis infection in humans. Future modelling efforts can incorporate interventions targeting humans and/or dogs to estimate the likely impact of different control strategies on disease burden.

The one reason for the literature gap in modelling the dynamics of S. stercoralis infection in humans, dogs and the environment is the uncertainties associated with the biology of the parasite. Moreover, a notable limitation identified in this review is the scarcity of data for parameterization of STH models. This data limitation introduces parameter uncertainty, potentially resulting in significant disparities between model predictions and actual data. Furthermore, consideration of fixed age groups, and less attention to environmental reservoir were mainly acknowledged.

This scoping review provides a comprehensive overview of the existing literature to identify the structures and mechanisms that describe STH transmission dynamics and critical gaps in the current literature on STH infection transmission modelling, particularly with S. stercoralis infection. With this focus, the review did not critically appraise each article to consider whether it was ‘fit-for-purpose’. Some modelling studies described in review articles (Anderson et al., 2014; Truscott et al., 2016) and book chapters (Anderson and May, 1991) were not included in the study, and hence, some unique features may have been missed relevant to S. stercoralis, although we consider this unlikely.

Conclusion

Control of S. stercoralis infection has been complicated by diagnostic challenges. However, WHO has recognized the significance of controlling S. stercoralis infection, incorporating preventive chemotherapy strategies into their publication ‘Ending the Neglect to Attain the Sustainable Development Goals: A Road Map for neglected tropical diseases 2021–2030’. This map underscores the need to investigate the transmission dynamics and to develop effective control methods for S. stercoralis infection, as they can positively impact human and animal health.

The review identified several key insights: different methods for modelling interaction dynamics between hosts and the environment, with a focus on infection acquisition and transmission mechanisms; modelling parasite life cycle dynamics within hosts and the external environment, encompassing processes such as reproduction and maturation; exploring multi-host dynamics; and inclusion of a diverse range of host heterogeneities in models. Furthermore, approaches to incorporating seasonal effects on the environmental reservoir into the model and analysing preventive interventions were also identified. These findings, particularly the mathematical techniques used to incorporate the parasite's life cycle features into the model, offer valuable guidance for understanding and controlling S. stercoralis transmission. A remaining gap for the development of S. stercoralis models is parameter estimation, given the many uncertainties related to diagnostic sensitivities and limitations on the knowledge of basic S. stercoralis biology. Future models for S. stercoralis would benefit from exploration of parameter space that encompasses these uncertainties.