Introduction
Trichostrongylus spp. are among the most widespread and important gastrointestinal nematodes affecting both humans and livestock, with a direct life cycle and global distribution (Ahmed et al. Reference Ahmed, Roy, Hasan, Zim, Biswas and Talukder2023; Bhat et al. Reference Bhat, Tak, Malik, Ganai and Zehbi2023). These parasites primarily inhabit the gastrointestinal tract of ruminants, particularly sheep and cattle, and are responsible for substantial economic losses due to impaired productivity, weight loss, and mortality (Roberts and Janovy Reference Roberts and Janovy2012). Importantly, Trichostrongylus also pose a significant zoonotic threat, particularly in pastoral and rural settings where humans live in close proximity to livestock and sanitation is limited (Aloui et al. Reference Aloui, Ghodhbane, Zaabi, Naija, Trabelsi and Bouchekoua2025; Wilczyńska and Korzeniewski Reference Wilczyńska and Korzeniewski2024). Human infection typically occurs through the consumption of raw or poorly washed vegetables contaminated with infective third-stage larvae (L3), which can survive in the environment for prolonged periods (Audebert et al. Reference Audebert, Cassone, Kerboeuf and Durette-Desset2003; Levine and Andersen Reference Levine and Andersen1973; Ralph et al. Reference Ralph, O’Sullivan, Sangster and Walker2006). Clinically, human trichostrongyliasis is often asymptomatic at low parasite load but may present with abdominal pain, diarrhoea, anorexia, nausea, eosinophilia, and mild anaemia in heavier infections (Buonfrate et al. Reference Buonfrate, Angheben, Gobbi, Mistretta, Degani and Bisoffi2017; Ghanbarzadeh et al. Reference Ghanbarzadeh, Saraei, Kia, Amini and Sharifdini2018; Watthanakulpanich et al. Reference Watthanakulpanich, Pongvongsa, Sanguankiat, Nuamtanong, Maipanich, Yoonuan, Phuphisut, Boupha, Moji, Sato and Waikagul2013). According to early estimates, up to 48 million people may have been infected globally (Watson Reference Watson1953).
Despite its wide distribution and recognized zoonotic potential, Trichostrongylus has received limited attention in global public health agendas; its temporal dynamics and future prevalence remain poorly characterized. Anticipating future trends in infection prevalence is therefore critical for designing timely and targeted interventions, optimizing the use of public health and veterinary resources, and reducing disease burden. In this context, mathematical and statistical modelling provides valuable tools for forecasting disease trends and informing policy decisions. Time series models, such as the autoregressive integrated moving average (ARIMA) model, are well suited for this purpose. Originally developed for economic forecasting, ARIMA has been applied in epidemiology to analyze time-dependent patterns in parasitic and infectious diseases (Rahmanian et al. Reference Rahmanian, Bokaie, Haghdoost and Barooni2020; Zhou et al. Reference Zhou, Ren, He, Hou and Deng2020). By leveraging historical prevalence data, these models can provide both short- and long-term projections to support evidence-based planning and enhance preparedness (Zhang et al. Reference Zhang, Diao, Yu, Pei, Lin and Chen2020).
In this study, we aimed to assess the temporal dynamics of Trichostrongylus infection in humans, ovines, and bovines using ARIMA models. Based on prevalence data collected over more than six decades, we constructed time series models for each host and forecasted infection trends from 2025 to 2034. These projections provide a descriptive baseline for long-term transmission patterns and may inform planning of surveillance, prevention, and control.
Materials and methods
Data collection
To support time-series forecasting, data on Trichostrongylus infection prevalence were extracted from published literature reporting time-specific prevalence information. Studies were included if they provided year-specific prevalence data for humans, ovines, or bovines. A comprehensive search was conducted in Web of Science, PubMed, ScienceDirect, Scopus, and Google Scholar using the keywords: (“Trichostrongylus” OR “trichostrongyliasis”) AND (“prevalence” OR “epidemiology”). The search covered publications from database inception to 18 February 2025. Data were compiled into a time series according to the year of sample collection as reported in each study (Table S1). Only studies presenting sufficient temporal resolution were retained for model construction. Discrepancies in data interpretation were resolved through team discussion. Studies were screened in multiple stages following a structured selection process. After removing duplicates, titles and abstracts were first reviewed for relevance, followed by a full-text evaluation of potentially eligible articles. Studies were excluded if they lacked year-specific prevalence data, were not focused on Trichostrongylus spp., involved non-target hosts, or did not provide sufficient epidemiological information for time series construction.
ARIMA models
A time series is defined as a sequence of data points recorded in chronological order (Fanoodi et al. Reference Fanoodi, Malmir and Jahantigh2019). The objective of time series analysis is to extract meaningful patterns from historical data and use these insights to forecast future values (Anghinoni et al. Reference Anghinoni, Zhao, Ji and Pan2019; Benvenuto et al. Reference Benvenuto, Giovanetti, Vassallo, Angeletti and Ciccozzi2020; He and Tao Reference He and Tao2018; Liu et al. Reference Liu, Liu, Jiang and Yang2011). Among the most widely used models for this purpose is the ARIMA model, originally developed by Box and Jenkins in the 1970s (Parzen Reference Parzen1982). ARIMA is particularly effective for modelling time-dependent processes as it accounts for trends, seasonal fluctuations, and random disturbances. In the ARIMA framework, the parameters p, d, and q represent the order of autoregression, the degree of differencing, and the order of the moving average, respectively. Depending on these parameters, ARIMA can function as a simplified AR, MA, I, or ARMA model (Li et al. Reference Li, Zhang, Zhang and Liu2019).
In this study, annual time series data on Trichostrongylus infection rates were compiled separately for humans (1947–2024), ovines (1966–2024), and bovines (1962–2024). Infection rates were expressed as percentages, and no additional transformations were applied prior to modelling. To visualize the global distribution of Trichostrongylus infection rates, spatial maps were created. These maps were generated using the R packages sf, rnaturalearth, and viridis. Infection rates for humans, ovines, and bovines were mapped separately, with each country shaded according to the infection prevalence in that region. To ensure data continuity, missing values were addressed prior to modelling. The Kalman smoothing technique, implemented within a state-space framework, was applied to interpolate missing data and reduce noise (Niako et al. Reference Niako, Melgarejo, Maestre and Vatcheva2024). Missing years accounted for approximately 16.0% of the human dataset, 11.9% of the ovine dataset, and 19.2% of the bovine dataset. To verify that smoothing did not distort long-term temporal trends, a sensitivity analysis was conducted by comparing raw and smoothed time series using Pearson correlation (r) and a slope-difference test (value ~ Year × series). The SSModel and KFS functions from the KFAS package in R were used for state estimation and smoothing. This method leverages information from both preceding and succeeding time points to generate a more accurate and continuous time series. By correcting for missing values and reducing short-term fluctuations, the resulting smoothed datasets provide a robust foundation for stable ARIMA model fitting and reliable long-term trend forecasting.
The ARIMA modelling process followed a structured approach consisting of model identification, parameter estimation, diagnostic evaluation, and forecasting (Lukman et al. Reference Lukman, Rauf, Abiodun, Oludoun, Ayinde and Ogundokun2020). To capture underlying linear trends in the data, all models were fitted with a drift term. The stationarity of each time series was assessed using the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test (Iranmanesh and Jalaee Reference Iranmanesh and Jalaee2021). Additionally, autocorrelation function (ACF) and partial autocorrelation function (PACF) plots were examined to evaluate stationarity and detect any potential seasonal patterns (He and Tao Reference He and Tao2018). When non-stationarity was indicated by significant KPSS test results and slowly decaying ACF plots, first-order differencing was typically applied. If required, higher-order differencing was also considered. Although seasonal lags were evaluated in the ACF and PACF plots, no consistent seasonal structure was observed, so seasonal differencing was not applied.
Model parameters (p, d, q) were determined based on the patterns observed in the ACF and PACF plots of the stationary series. A range of candidate ARIMA models was fitted for each host species. Model performance was assessed using multiple criteria, including the Bayesian information criterion (BIC), the coefficient of determination for stationary data (Stationary R2), and in-sample forecast accuracy metrics such as root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) (Ceylan Reference Ceylan2020; He and Tao Reference He and Tao2018). To evaluate residual independence, the Ljung-Box Q test was applied. Final model selection for each species was guided by a combination of model parsimony, goodness-of-fit, residual diagnostics, and forecasting performance. Separate ARIMA models were developed for each host species, including humans, ovines, and bovines, to capture the unique epidemiological dynamics of Trichostrongylus infection in these hosts. Each model was trained using the processed and smoothed time series data and used to forecast infection trends from 2025 to 2034.
All statistical analyses and visualizations were performed in RStudio (R version 4.4.2; RStudio version 2024.10.31) using the following packages: KFAS (v1.6.0), forecast (v8.24.0), ggplot2 (v3.5.2), dplyr (v1.1.4), zoo (v1.8.14), extrafont (v0.19), sf (v1.0.21), rnaturalearth (v1.0.1), and viridis (v0.6.5). Model performance was assessed through several metrics, including Stationary R2, RMSE, MAE, MAPE, BIC, and the Ljung-Box Q test. Statistical significance was considered at p < 0.05 where applicable, while diagnostic tests such as the Ljung-Box Q test were interpreted based on the absence of significant autocorrelation in model residuals.
Results
A total of 12,709 records were retrieved from five major databases. After removing duplicates and conducting title/abstract screening, 3,578 articles were assessed at the full-text level. Based on predefined inclusion criteria, 240 studies were finally included in the ARIMA analysis. These studies spanned 60 countries and provided annual prevalence data covering over six decades (Figure 1). Of these, 84 studies focused on humans, 61 on bovines, and 118 on ovines. It is important to note that some studies were included for multiple host species, leading to potential overlap in the data. A complete list of included references is available in the Supplementary Materials.
Flow diagram of the literature search strategy.
The global prevalence of Trichostrongylus infection varied widely across hosts and countries. Overall, humans showed the lowest prevalence compared with ovines and bovines. Among humans, higher values were observed in Iraq (4.34%), Sudan (2.53%), and Peru (2.07%), whereas lower values occurred in Nicaragua (0.05%) and the United Arab Emirates (0.03%). In ovines, prevalence was highest in Czechia (87.50%), the United States (82.50%), and Australia (79.67%), and lower in Jordan (7.00%), Ghana (5.58%), and Uganda (2.16%). For bovines, the highest values were recorded in Austria (100.00%), Germany (96.43%), and Australia (85.38%), with lower values in Bangladesh (4.50%), Colombia (3.02%), and Ghana (2.74%). These country-level patterns are mapped in Figure 2 and listed in full in Table S2.
Global prevalence of Trichostrongylus infection across different host species. A humans. B ovines. C bovines.
Autocorrelation estimates for the time series of human, ovine, and bovine Trichostrongylus infections are presented in Figure 3. The dashed lines represent two standard deviations from zero, providing a threshold to identify statistically significant autocorrelations. Figure 4 overlays the original and Kalman-smoothed series for humans, ovines, and bovines. Concordance was high (humans: r = 0.979, slope-difference p = 0.997; ovines: r = 0.915, p = 0.993; bovines: r = 0.983, p = 0.981). Overall, Kalman smoothing preserves long-term trends while attenuating short-term variability, and no clear seasonality is evident across hosts.
Plots of ACF (A humans. B ovines. C bovines) and PACF (D humans. E ovines. F bovines), the annual infection rate of Trichostrongylus across different species.
Kalman-smoothed temporal trends and sensitivity to smoothing for Trichostrongylus prevalence. Panels overlay the original series (blue) and the Kalman-smoothed series (red) for humans, ovines, and bovines. Each panel reports the Pearson correlation (r) and the p-value from a slope-difference test comparing the smoothed and original series. A humans. B ovines. C bovines.
Stationarity of the time series was assessed using the KPSS test, with results summarized in Table 1. All p-values exceeded 0.05, suggesting that the null hypothesis of stationarity could not be rejected at the 5% significance level. However, the ACF and PACF plots revealed slowly decaying autocorrelations in the human and bovine time series, indicating potential non-stationarity (Figure 3A, C, D, F). As a result, an additional round of differencing was applied to these two series prior to ARIMA modelling. In contrast, the ovine time series exhibited stationarity following the initial differencing step, likely due to the more stable and less volatile nature of ovine infection rates. This greater stability of the ovine data meant that an autoregressive model was more appropriate, as no further differencing was required. ARIMA model parameters were initially identified using ACF and PACF plots derived from the stationary time series (Figure 5). Based on these diagnostics, a set of candidate models was proposed for each host species, including humans, ovines, and bovines (Table 2). The final model selection was based on both ACF and PACF plots, along with a thorough evaluation of model performance metrics.
KPSS test results for stationarity of Trichostrongylus infection rate time series in different hosts
Time series, ACF, and PACF plots of first-order differenced Trichostrongylus infection rates. A humans time series. B ACF for humans. C PACF for humans. D bovines time series. E ACF for bovines. F PACF for bovines.
Comparison of tested ARIMA models
For humans, the selected ARIMA(0,1,1) model demonstrated strong forecasting ability, with a high Stationary R2 of 0.9772, RMSE of 0.4129, and MAE of 0.3048. Although the MAPE was relatively high at 76.77%, this was likely influenced by low prevalence values in some years, such as when the infection rate was close to 0% or below 2% (e.g., in 2005, 2016, and 2018). It is important to note that MAPE tends to be unstable when prevalence values are very low. A sensitivity test excluding near-zero prevalence years confirmed that the model still showed good performance, with similar results in terms of RMSE and MAE. The Ljung-Box Q test yielded a p-value of 0.9941, indicating no significant autocorrelation in the residuals and confirming the adequacy of the model. The ovine time series was best represented by an ARIMA(3,0,0) model, which showed solid performance metrics: Stationary R2 of 0.8389, RMSE of 0.3696, MAE of 0.2721, and a notably low MAPE of 7.26%, indicating high predictive accuracy. The residuals passed the Ljung-Box test (p = 0.9671), suggesting no significant autocorrelation. For bovines, the ARIMA(0,1,1) model provided the best fit, with a Stationary R2 of 0.9745, RMSE of 2.2564, MAE of 1.5204, and MAPE of 10.29%. The Ljung-Box test result (p = 0.9933) confirmed that the residuals were uncorrelated and resembled white noise, further validating model adequacy (Table 3).
Statistical validation of ARIMA models
Overall, the ARIMA models selected for all three host species demonstrated good fit, robust residual diagnostics, and strong forecasting performance (Figures 6 and 7). Parameter estimates for each model are presented in Table 4. Most coefficients were statistically significant (p < 0.05), supporting the explanatory power of the models. One exception was the third autoregressive term (AR3) in the ovine model (p = 0.0609), which was retained due to its contribution to model performance. Forecasts from the selected ARIMA models revealed distinct temporal trends across the three host groups (Figure 7 and Table 5). In humans, infection rates are projected to decline steadily over the next decade, decreasing from 4.64% (95% CI: 2.34% to 8.62%) in 2025 to 3.73% (95% CI: 0.04% to 52.28%) in 2034. This consistent downward trend suggests a continued reduction in human infection risk. For ovines, the model forecasts a gradual increase in infection rates, from 6.50% (95% CI: 3.52% to 11.48%) in 2025 to 15.56% (95% CI: 3.77% to 51.29%) by 2034. The rate of increase initially accelerates before stabilizing, indicating a growing parasite pressure in ovine populations that eventually plateaus at a steady level. In contrast, the bovine forecast shows a long-term decline. Infection rates are expected to drop from 20.11% (95% CI: 12.69% to 28.05%) in 2025 to 11.76% (95% CI: -15.63% to 49.50%) by 2034. Due to limited data, these predictions were made using the full dataset without independent validation (no split-sample or rolling-origin evaluation).
Estimated ACF (A ARIMA(0,1,1) for humans. B ARIMA(3,0,0) for ovines. C ARIMA(0,1,1) for bovines) and PACF (D ARIMA(0,1,1) for humans. E ARIMA(3,0,0) for ovines. F ARIMA(0,1,1) for bovines) plots to predict the epidemiological trend of Trichostrongylus prevalence.
ARIMA-fitted Trichostrongylus infection time series and forecasted infection rate for different species. A ARIMA(0,1,1)-fitted human infection rate time series (1947–2024). B ARIMA(3,0,0)-fitted ovine infection rate time series (1966–2024). C ARIMA(0,1,1)-fitted bovine infection rate time series (1962–2024). Red, blue, and green lines represent the fitted curve of the constructed model, the observed infection rate, and the forecast curve of the constructed model (2025–2034), respectively.
Parameters of ARIMA models
a p < 0.05.
Predicted Trichostrongylus infection rates in different hosts (2025–2034) using ARIMA models with 95% CI
Discussion
This study applies ARIMA to forecast future trends of Trichostrongylus infection across humans, ovines, and bovines using published prevalence data, estimating host-specific trajectories and their implications for transmission (Anokye et al. Reference Anokye, Acheampong, Owusu and Isaac-Obeng2018).
For humans, the model forecasts a continued decline in infection rates, from 4.64% in 2025 to 3.73% by 2034, extending the downward trend observed in recent decades. Although this absolute reduction is small, it may be consistent with gradual improvements in sanitation, reduced reliance on night soil, expanded access to healthcare, and increased public awareness of zoonotic helminth infections in endemic regions. However, causal drivers cannot be inferred from ARIMA, and the wide forecast intervals suggest limited short-term biological impact. Even so, the trajectory is favourable and could compound over longer horizons. Advances in diagnostics and parasitology may also influence reported prevalence. These factors were not explicitly modelled in our analysis. (Frickmann et al. Reference Frickmann, Schwarz, Rakotozandrindrainy, May and Hagen2015; Ishida et al. Reference Ishida, Rubinsky-Elefant, Ferreira, Hoshino-Shimizu and Vaz2003; Pilotte et al. Reference Pilotte, Papaiakovou, Grant, Bierwert, Llewellyn, McCarthy and Williams2016).
A comparable downward trend is projected in bovines, with infection rates from 20.11% in 2025 to 11.76% by 2034. Although causality cannot be inferred from ARIMA, this trajectory is plausibly linked to animal-level and herd-level factors. In bovine populations, prevalence is more directly influenced by herd management practices (e.g., housing versus extensive grazing, stocking density), pasture contamination and watering-point management, seasonal movement and market-driven animal trade, and the degree of implementation of biosecurity measures (Smithand et al. Reference Smith, Marion, Swain, White and Hutchings2009; VanderWaal et al. Reference VanderWaal, Gilbertson, Okanga, Allan and Craft2017). Economic incentives and the typically higher per-animal value of cattle can facilitate more consistent investment in veterinary care and coordinated control programmes, which may partly explain why bovine declines can be stronger or more uniform than those observed in ovines. Nevertheless, substantial regional heterogeneity persists, and structural constraints such as limited veterinary capacity, weak extension services, and environmental and socioeconomic barriers can hinder effective control in resource-limited settings (Lindahl and Grace Reference Lindahl and Grace2015; Thompson Reference Thompson2023).
By contrast, in ovines, a distinctly different pattern emerges. The ARIMA(3,0,0) model projects a steady rise in Trichostrongylus infection rates, increasing from 6.50% in 2025 to 15.56% by 2034. This divergence may be consistent with greater pasture exposure of small ruminants and less consistent application of parasite control relative to bovines. Given the role of ovines as key reservoirs and their heightened vulnerability due to constant exposure to contaminated pasture, proactive control strategies are essential, including rotational grazing, routine anthelmintic administration, and improved pasture hygiene. Broader environmental change, including climate variability and intensifying production systems, may further influence transmission and warrants cautious interpretation and targeted surveillance (Skuce et al. Reference Skuce, Morgan, van Dijk and Mitchell2013).
Climate factors such as temperature, humidity, and rainfall play a significant role in the survival and transmission of Trichostrongylus (Roeber et al. Reference Roeber, Jex and Gasser2013). These conditions affect larval development and viability and may help explain the heterogeneity observed across species and countries (Pandey et al. Reference Pandey, Chitate and Nyanzunda1993). In our dataset, comparisons within the same host species are consistent with higher prevalences in warm, humid regions: for ovines, prevalence is 76.15% in Sri Lanka and 70.21% in Brazil, whereas it is much lower in the more arid Middle Eastern setting of Jordan (7.00%); for bovines, prevalence reaches 55.48% in the humid temperate Netherlands and 43.46% in Brazil but is only 6.03% in arid Egypt and 0% in pastoral herds sampled in Kenya. In humans, very low prevalence is observed in the arid United Arab Emirates (0.03%) compared with higher estimates in more humid countries such as Peru (2.07%) and Vietnam (0.77%). These patterns are broadly consistent with limited parasite survival in hot, dry environments (Mas-Coma et al. Reference Mas-Coma, Valero and Bargues2008). The data also suggest that zoonotic risk in humans tends to be greater where animal infection rates are higher; for example, in the United States, ovine and bovine prevalences of 82.50% and 2.99%, respectively, co-occur with a human prevalence of 1.69%. Similar patterns are seen in Iran, where prevalences are 33.25% in ovines and 8.62% in bovines alongside 1.96% in humans, and in Iraq, where human prevalence reaches 4.34% with corresponding ovine and bovine prevalences of 9.00% and 11.12%, respectively. These observations are consistent with higher zoonotic risk in settings with greater infection pressure from ruminants, although climate and other covariates were not modelled explicitly here.
Future control strategies would benefit from integrating the veterinary, environmental, and human health sectors to effectively break the transmission cycles of Trichostrongylus. A collaborative, One Health approach could play an important role in addressing the complex interactions between humans, animals, and the environment, ensuring sustainable, long-term management of parasitic infections across all host species.
Our forecasts should be interpreted with caution because they are based solely on prevalence and do not capture infection intensity or clinical severity. They additionally relied on published data with uneven regional coverage, applied Kalman smoothing to impute missing years, and were evaluated in-sample only. Smoothing can introduce uncertainty, particularly when estimates come from limited or geographically localized sources, and overrepresentation of well-surveilled regions may bias global patterns. Limited data from certain regions could alter global forecasts if more information were available. Moreover, the relatively low number of studies included, particularly for bovines and humans, further limits the precision and robustness of the forecasts. This is especially critical in data-sparse regions. Future modelling efforts should integrate ecological variables such as rainfall, temperature, altitude, and land use patterns to enhance prediction accuracy. They should also assess ensemble modelling techniques and machine learning algorithms, and expand geographically balanced surveillance with wider adoption of molecular diagnostics to generate high-resolution, temporally aligned time series.
Conclusion
The ARIMA-based forecasts provide a cross-host view of the evolving epidemiology of Trichostrongylus. The observed divergence in predicted trends, with projected declines in humans and bovines, and a rise in ovines, suggests that host-specific factors and ecological contexts shape future transmission patterns. These findings support incorporating predictive modelling into national and regional parasite-control programs, together with strengthened surveillance and advanced diagnostics, to enable sustained reductions in prevalence.
Supplementary material
The supplementary material for this article can be found at http://doi.org/10.1017/S0022149X25101004.
Author contribution
Wei Wei: Writing – original draft, Visualization, Validation, Software, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Xiang Gu: Data curation, Formal analysis, Writing – review and editing. Rui Shi: Software, Formal analysis, Data curation, Methodology. Lu An: Formal analysis, Data curation. Rigai Sa: Data curation. Jing Li: Formal analysis. Hua Bai: Data curation. Risu Na: Formal analysis. Rui Wang: Writing – review and editing, Supervision, Funding acquisition, Methodology, Investigation, Conceptualization.
Funding sources
Funding for this study was provided by Key R & D and Achievement Transformation Projects of Inner Mongolia, China (grant no. 2023YFDZ0048), Research Project Funding for First-class Disciplines at Inner Mongolia Education Department (grant no. YLXKZX-NND-012), Technology Support Project of Major Innovation Platform (Base) Construction (grant no. KCX2024016), National Center of Technology Innovation for Dairy (grant no. 2023-JSGG-5), the Natural Science Foundation of Inner Mongolia, China (grant no. 2023LHMS03022, and 2023LHMS03005) and the National Natural Science Foundation of China (grant no. 32160838).
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical standard
This study did not require an ethical approval, as it was based on information/data retrieved from published studies already available in the veterinary public domain.
