Article

September 30, 2026

Predictive modeling for optimization of the Wolbachia method

Predictive Modeling for Optimization of the Wolbachia Method

Cecília Parolim Ferraz; Auberth Henrik Venson

DOI: 10.22167/2675-6528-202602798

Article derived from a Final Course Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

The optimization of the Wolbachia method for the control of Aedes aegypti is a relevant challenge in public health. The study analyzed the environmental, operational, and spatial factors that influenced the adherence of the Wolbachia bacterium in Aedes aegypti populations, aiming to optimize the quantity of mosquitoes released. It was conducted in the municipality of Joinville/SC, based on six monitoring campaigns between September and December 2024. Spatial, environmental, population, and operational data were integrated, using geoprocessing techniques to create influence areas of 300 meters around the monitoring points. The analysis employed a mixed-effects linear regression model to evaluate the influence of the explanatory variables on the proportion of mosquitoes with Wolbachia (wMel). The results indicated that adherence resulted from the interaction between environmental and operational factors, with a positive influence of relative air humidity and negative influence of population density, in addition to a positive effect of the quantity of mosquitoes released. A saturation behavior was identified, where increases in mosquito release did not generate proportional gains in adherence, especially in favorable scenarios. Scenario analysis demonstrated that the quantity of mosquitoes needed varied according to environmental and population conditions, being higher in unfavorable contexts. In advanced stages, environmental factors exerted greater influence on adherence than the intensity of release. The results reinforced the importance of adaptive strategies and highlighted the model’s potential as a support tool for the operational planning of releases.

Keywords: Spatial Analysis; Geoprocessing; Predictive modeling; Operational optimization; Wolbachia.

1. Introduction

Arboviruses represent a growing challenge for public health in tropical regions, such as Brazil, where environmental factors favor the proliferation of the Aedes aegypti mosquito. The World Health Organization (WHO) points out that dengue, one of the main arboviruses, causes more than 390 million infections annually globally, with its incidence expanding in densely populated urban areas. This increase is intrinsically linked to climate change, disordered urbanization, and increasing human mobility.

In this scenario, the Wolbachia method, developed by the World Mosquito Program, emerges as an innovative approach to mitigate the transmission of these diseases. The strategy involves releasing Aedes aegypti mosquitoes infected with the Wolbachia bacterium, which has the ability to reduce the mosquito’s vector competence for transmitting viruses such as dengue, zika, and chikungunya. The effectiveness of this method was demonstrated in Niterói, Rio de Janeiro, where a reduction of up to 69% in dengue cases, 56% in chikungunya, and 37% in zika was observed (Utomo et al., 2021; Ryckebusch et al., 2024).

Despite promising results in various locations, the large-scale implementation and optimization of the Wolbachia method require a deep understanding of the factors influencing the bacterium’s adherence in mosquito populations. The program’s expansion in Brazil, in partnership with the Ministry of Health and the World Mosquito Program, includes the municipality of Joinville, Santa Catarina. In this context, the need for innovative vector control strategies is reinforced by the significant increase in Aedes aegypti foci in Joinville, which rose from 292 in 2017 to 9,453 in 2021 (Joinville, 2022). Optimizing the quantity of mosquitoes released becomes crucial for the operational efficiency and sustainability of the program.

This research adopts a predictive modeling approach, based on supervised learning, to analyze the relationship between environmental, operational, and spatial variables and the proportion of mosquitoes with Wolbachia (wMel). The study was conducted in the municipality of Joinville, which has approximately 650,000 inhabitants and a humid subtropical climate (IBGE, 2024). Empirical data were collected during six monitoring campaigns conducted between September and December 2024, integrating spatial, environmental, population, and operational information through geoprocessing techniques, including the delimitation of 300-meter influence areas around the monitoring points.

Understanding these factors is essential for improving mosquito release strategies, optimizing resource use, and maximizing vector control effectiveness. This work aimed to analyze the relationship between environmental and operational variables, such as climatic conditions and release parameters, and Wolbachia adherence levels in Joinville/SC, seeking to develop a predictive model capable of simulating scenarios of reduced mosquito release quantities, while maintaining or maximizing bacterial adherence.

2. Material and Methods

The present research adopted a predictive modeling approach, based on

Learning under supervision

, to analyze the relationship between environmental, operational, and spatial variables and the proportion of mosquitoes with Wolbachia (wMel). The study was quantitative and exploratory in nature, seeking to identify patterns and relationships between variables to optimize the number of mosquitoes released in the vector control program.

The study area comprised the municipality of Joinville, in Santa Catarina, which has a humid subtropical climate and approximately 650,000 inhabitants (IBGE, 2024). The empirical data collection was carried out during six monitoring campaigns, which occurred between September and December 2024, covering fixed monitoring points distributed throughout the region.

For the construction of the analytical database, each observation corresponded to a fixed monitoring point, identified by a unique code. This longitudinal structure allowed for repeated monitoring of the points over time. The response variable used was the proportion of mosquitoes with Wolbachia (wMel), expressed on a continuous scale from zero to one.

The explanatory variables considered included operational, demographic, and environmental factors. Among them, the quantity of mosquitoes released (qtdMosq), the population in the vicinity of the monitoring points (qtdPop), the relative humidity of the air (umidAr), and the total number of mosquitoes analyzed (total_count) stood out, the latter being used as a measure of sample size.

The process of constructing the analytical base involved geoprocessing steps for the spatial integration and aggregation of variables. For each monitoring point, an area of influence with a radius of 300 meters was defined, representing the immediate surroundings of mosquito activity. From this spatial unit, information from various databases was aggregated, including population, environmental, and operational data.

The spatial variables were derived through spatial analysis operations, which included the creation of buffers, intersection with census tracts, and attribute aggregation. This methodology ensured that each observation reflected the specific local conditions of the monitoring point, incorporating spatially contextualized information into the model.

In the data preparation and treatment stage, exploratory spatial representations were developed, available in Annexes A, B, C, D, and E of the original TCC, to validate and understand the initial data structure. Subsequently, the database was imported into the Python environment, where cleaning and organization of records were performed.

A numerical shipment variable (remessa_num) was created, extracted from the textual identifier of the campaigns, and its categorical version (remessa_cat), used in the modeling to represent temporal effects. The selected continuous variables were standardized by z-score, aiming for comparability between coefficients and numerical stability in model fitting.

Before the implementation of the final model, a multicollinearity analysis was conducted among the initially considered variables. The correlation matrix and the Variance Inflation Factor (VIF) were used for this evaluation. Based on the results, the variables with the greatest theoretical relevance and interpretability for the study were selected.

The implemented predictive algorithm was a linear mixed-effects regression model, suitable for the data structure with repeated measures per monitoring point. In the fixed-effects component, the standardized variables qtdMosq, qtdPop, umidAr, total_count, and the categorical variable remessa_cat were included.

In the random component of the model, an intercept was considered per monitoring point (identifier), with the objective of capturing the unobserved variability between points. The computational implementation of the model was carried out using the Python programming language, with the aid of the `statsmodels.formula.api.mixedlm` library.

After model adjustment, diagnostics were generated based on the analysis of residuals and the comparison between observed and fitted values, allowing for the evaluation of the model’s adequacy to the data. Exploratory and diagnostic graphs were also constructed to check for patterns and possible deviations.

Additionally, predictive scenarios were simulated with different combinations of environmental and population variables, classified as favorable, intermediate, and unfavorable. For each scenario, the quantities of mosquitoes necessary to achieve adherence levels of 70%, 80%, 90%, and 100% were estimated, contributing to the operational analysis of the method.

Finally, a specific analysis of the last monitoring campaign (shipment six) was performed, using simple linear regression. The objective was to investigate possible saturation effects in the system at more advanced stages of implementation, complementing the understanding of the Wolbachia adherence dynamics.

3. Results and Discussion

This section details the research findings on the optimization of the Wolbachia method for the control of Aedes aegypti in Joinville/SC, interpreting the results in light of the proposed objectives and applied methodology. The data revealed the complex interaction between environmental, operational, and demographic factors in the bacterium’s adherence, with significant implications for the planning and execution of mosquito release campaigns. The analysis allowed for the identification of crucial patterns and the development of a predictive model capable of simulating scenarios and optimizing the quantity of mosquitoes released, aiming for maximum program effectiveness and sustainability.

Initially, it was observed that Wolbachia adherence does not behave linearly in relation to the quantity of released mosquitoes, being influenced by a range of variables. This understanding is fundamental to refining vector control strategies, moving away from generic approaches in favor of interventions more adapted to local realities. The ability to predict adherence in different contexts allows for a more efficient allocation of resources, maximizing the impact of public health actions in combating arboviruses.

Spatial contextualization of the study area

The study was conducted in the municipality of Joinville, focusing on areas designated for the operation of releasing mosquitoes with Wolbachia. The spatial distribution of monitoring points, represented by the ovitraps used in the sixth collection campaign, revealed a notable concentration in urbanized regions. This distribution reflects a strategic prioritization of areas with higher population density, where the proliferation of Aedes aegypti and the transmission of arboviruses tend to be more intense. The influential population within a 300-meter radius around each monitoring point varied, with classes ranging from 111 to 2821 inhabitants, indicating the demographic diversity of the areas under intervention.

The analysis of the spatial coverage of the sampling units demonstrated that the 300-meter influence areas around the monitoring points significantly overlap. This overlap resulted in continuous coverage in regions with higher point density, reinforcing the spatial representativeness of the data used in the modeling. Such spatial detail was crucial for capturing the specific local conditions that could influence the dynamics of Wolbachia dispersion and establishment, providing a robust basis for subsequent analyses.

The level of spatial detail adopted in the construction of the explanatory variables was high, incorporating elements such as building density and the extent of water bodies within a 300-meter radius of each monitoring point. This approach allowed for a more granular understanding of the relationship between the physical environment and Wolbachia adherence. The integration of this contextual information was essential for the development of a predictive model that considered the particularities of each locality, going beyond a purely aggregated analysis.

Model performance

The developed linear mixed-effects regression model demonstrated adequate capacity to represent the complex relationship between the explanatory variables and Wolbachia adherence. The comparison between observed values and values adjusted by the model indicated good overall fit, especially in the range of higher values for the proportion of mosquitoes with Wolbachia (wMel). This suggests that the model has greater precision in scenarios where Wolbachia stabilization is already in an advanced stage, which is a relevant finding for the operational management of the program.

The model’s robustness in predicting adherence at higher levels of wMel is particularly useful for long-term planning, where the goal is to maintain the bacteria at high levels in the mosquito population. Although overall adherence was satisfactory, the model’s performance across different adherence ranges points to the need to consider the program’s implementation phases when applying predictions. The ability to identify high stabilization scenarios allows for directing resources towards maintaining adherence, while in initial phases, other strategies may be more suitable.

Model diagnosis

The analysis of residuals was performed to evaluate the model’s adequacy, revealing that the error variability did not remain constant across the range of predicted values. It was observed that the dispersion of residuals was greater at intermediate levels of adherence, suggesting heteroscedasticity in certain ranges of the response variable. This characteristic indicates that the precision of predictions may vary depending on the level of Wolbachia adherence, potentially being less precise in transitional or less stabilized stages.

The distribution of the residuals showed a concentration close to zero, which is a positive indication of the absence of systematic bias in the model. However, a negative asymmetry was observed in the distribution, pointing to a higher frequency of negative errors. This means that the model tended to overestimate adherence in some situations, although the magnitude of these errors did not compromise the general applicability of the model for predictive purposes. Understanding these residual characteristics is essential for interpreting the predictions with due caution and for future model improvements.

Despite the characteristics observed in the residual analysis, the model proved to be adequate for predictive purposes, especially considering the nature of the response variable, which is limited to the interval between 0 and 1. The model’s ability to capture the dynamics of Wolbachia adherence, even with some variability in the error, reinforces its utility as a decision support tool. The interpretation of the results, therefore, is not based exclusively on statistical significance tests, but also on the coherence of the observed effects and the operational applicability of the identified patterns.

Relationship between variables and Wolbachia adherence

The analysis of the relationship between the population around the monitoring points and Wolbachia adherence revealed a negative trend. This finding suggests that in environments with higher population density, the establishment of the bacteria may be more challenging. Such difficulty can be attributed to the greater ecological complexity and vector population dynamics in these contexts, where factors such as breeding site availability, human mobility, and mosquito genetic diversity may influence the infection rate and Wolbachia dispersion.

On the other hand, the number of released mosquitoes showed a positive relationship with Wolbachia adherence, indicating that an increase in mosquito release contributes to a higher proportion of infected individuals. However, high data dispersion was observed, suggesting that adherence does not depend exclusively on the intensity of release. This dispersion reinforces the idea that other factors, such as environmental conditions and population density, interact with the number of released mosquitoes to determine the success of the intervention.

Relative air humidity also showed itself to be a variable with a positive influence on Wolbachia adherence, while population density exerted a negative influence. These results underscore the importance of considering climatic and demographic conditions when planning release campaigns. Environments with higher relative humidity may favor the survival and reproduction of infected mosquitoes, while densely populated areas may present additional challenges for the stabilization of the bacteria, requiring adjustments in release strategies.

Temporal effect

The analysis of Wolbachia adherence over the monitoring shipments showed a temporal evolution behavior of the system. The initial shipments, particularly the second one, presented greater variability and a wide dispersion of adherence values. This suggests that, in the initial phases of program implementation, the stabilization of the bacteria in the mosquito population is more heterogeneous and susceptible to fluctuations, reflecting the introduction and adaptation phase of the system.

In contrast, the most recent remittances demonstrated a higher concentration of values close to maximum adherence, with the proportion of mosquitoes with Wolbachia (wMel) tending towards 1. This pattern indicates a clear trend of process stabilization over time. Such behavior suggests a cumulative effect of successive releases, resulting in higher and more consistent adherence levels in the more advanced phases of the program. This finding reinforces the hypothesis that the introduction of Wolbachia is a progressive process, depending on the continuity and persistence of releases over time to achieve the desired stability.

Scenario analysis

Scenario analysis allowed quantifying the number of mosquitoes needed to achieve different levels of Wolbachia introgression under distinct environmental and population conditions. The results indicated that, in favorable scenarios, smaller quantities of mosquitoes are sufficient to reach the desired introgression levels. For example, for introgression targets of 0.7, 0.8, 0.9, and 1.0 in favorable scenarios, the required number of mosquitoes was 6,198.

In intermediate scenarios, a gradual increase in operational necessity was observed. For adherence targets of 0.7, 0.8, and 0.9, the mosquito quantity remained at 6,198. However, to achieve an adherence of 1.0 in intermediate scenarios, the required mosquito quantity increased significantly to 89,578. This variation highlights the system’s sensitivity to environmental and population conditions, even in contexts not considered entirely unfavorable.

In unfavorable scenarios, the required mosquito quantities were significantly higher. For adherence targets of 0.7 and 0.8, the quantity was 6,198, but for 0.9, it rose to 45,789, and for 1.0, it reached 184,956 mosquitoes. These data reinforce the importance of adapting release strategies to local conditions, avoiding a one-size-fits-all approach that can be inefficient in more challenging contexts. The ability to estimate these quantities allows for more precise and optimized resource planning.

Regardless of the scenario, the analysis revealed a saturation behavior, where additional increases in the quantity of mosquitoes released result in reduced gains in adherence. This saturation effect indicates that there is a point beyond which intensifying releases does not generate proportional increments in the proportion of mosquitoes with Wolbachia. Understanding this limit is crucial to avoid wasting resources and to focus on other strategies when the system approaches its equilibrium point.

Analysis of shipment 6 and saturation effect

The specific analysis of batch 6, which corresponds to the most advanced stage of the intervention, clearly showed the saturation effect of the system. The relationship between the number of mosquitoes released and the Wolbachia adherence in this batch showed a reduced slope, indicating the presence of decreasing marginal gains. This means that, in more mature phases of the program, for each additional mosquito released, the increase in bacterial adherence is smaller, characterizing a point of diminishing returns.

This behavior suggests that, at high levels of adherence, the system tends towards an equilibrium state, where further increases in release intensity have a limited impact. In other words, beyond a certain threshold, the mosquito population is already largely infected, and the introduction of more mosquitoes with Wolbachia does not result in a significant change in the overall proportion. This observation is vital for operational optimization, as it directs attention towards maintaining adherence rather than an indefinite increase in the number of releases.

The identification of this saturation effect in the most advanced stage of monitoring has important practical implications. It suggests that, in advanced stages of implementation, environmental factors may exert a greater influence on Wolbachia adherence than the release intensity itself. This implies that, once a certain level of stabilization is reached, program management should focus more on adapting to environmental conditions and maintaining adherence, rather than simply increasing the number of mosquitoes released.

In general, the results obtained demonstrate that Wolbachia adherence is influenced by multiple factors and presents a non-linear behavior, which requires an adaptive approach in planning interventions. The developed model proved adequate for predictive and operational purposes, allowing the identification of relevant relationships between variables such as relative air humidity, population density, and the quantity of mosquitoes released. The main contribution of the study lies in the identification of the saturation effect and the possibility of estimating more efficient release quantities, considering different environmental and operational scenarios, which directly addresses the objective of optimizing the quantity of mosquitoes released while maintaining or maximizing bacterial adherence.

4. Conclusion

This study aimed to analyze the relationship between environmental, operational, and spatial variables and the proportion of mosquitoes with Wolbachia (wMel) in Joinville/SC, seeking to optimize the quantity of mosquitoes released. It was found that Wolbachia adherence resulted from the complex interaction between factors such as relative air humidity, which exerted a positive influence, and population density, which demonstrated a negative effect. It was also observed that the quantity of mosquitoes released positively impacted adherence; however, a saturation behavior was identified, where additional increases in release did not generate proportional gains, especially in favorable scenarios. Scenario analysis showed that the quantity of mosquitoes needed to achieve adherence goals varied significantly according to environmental and population conditions, being higher in unfavorable contexts. In advanced stages of the program, environmental factors began to exert greater influence on adherence than the intensity of release. The main practical contribution of this work lies in the development of a predictive model capable of simulating scenarios and estimating more efficient release quantities, supporting operational planning and the optimization of resource use in vector control.

Despite the model’s robustness in predicting adherence at higher levels of wMel, heteroscedasticity of residuals at intermediate adherence levels was identified as a limitation, suggesting lower precision in transition phases. Additionally, residual analysis indicated a tendency for the model to overestimate adherence in some situations, and the dependence on data quality and the spatio-temporal variability of environmental conditions were recognized. For future studies, it is suggested to improve the model to mitigate heteroscedasticity and investigate the influence of unobserved factors that may impact Wolbachia adherence, as well as explore adaptation strategies to environmental conditions in advanced stages of the program. Such investigations can further refine mosquito release strategies, maximizing the effectiveness and sustainability of the Wolbachia method.

Bibliographic References

INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA (IBGE). Cidades: Joinville (SC). 2024. Disponível em: <https://cidades.ibge.gov.br/brasil/sc/joinville/panorama>. Acesso em: 28 out. 2025.

JOINVILLE (SC). Plano Municipal de Saúde de Joinville: 2022–2025. Joinville: Secretaria Municipal da Saúde, 2022. Disponível em: <https://www.joinville.sc.gov.br/wp-content/uploads/2022/11/Plano-Municipal-de-Saude-de-Joinville-2022-2025-versao-final.pdf>. Acesso em: 1 nov. 2025.

RYCKEBUSCH, F. et al. Effectiveness of Wolbachia-infected mosquito deployments in reducing the incidence of dengue and other Aedes-borne diseases in Niterói, Brazil: a quasi-experimental study. The Lancet Global Health, v. 12, n. 2, p. e301-e311, 2024. DOI: 10.1016/S2214-109X(23)00414-8.

UTOMO, S. et al. Effectiveness of Wolbachia-infected mosquito deployments in reducing the incidence of dengue and other Aedes-borne diseases in Niterói, Brazil: a quasi-experimental study. PLoS Global Public Health, v. 1, n. 7, e0000039, 2021. DOI: 10.1371/journal.pgph.0000039.

Article originating from the Final Course Work of the Specialization in Data Science and Analytics of the MBA USP/Esalq

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