F1000Research F1000Research 2046-1402 F1000 Research Limited London, UK 10.12688/f1000research.169601.1 Method Article Articles Graph-based epidemic modeling of West Nile Virus: Forecasting and containment

[version 1; peer review: 1 approved, 1 approved with reservations, 1 not approved]

 Branda Francesco Conceptualization Data Curation Formal Analysis Methodology Writing – Original Draft Preparation Writing – Review & Editing https://orcid.org/0000-0002-9485-3877 1 2 Ahmed Mohamed Mustaf Writing – Review & Editing https://orcid.org/0009-0006-5991-4052 a 3 Defilippo Annamaria Writing – Original Draft Preparation Writing – Review & Editing 4 Lomoio Ugo Writing – Original Draft Preparation Writing – Review & Editing https://orcid.org/0000-0001-8150-0039 4 Puccio Barbara Writing – Original Draft Preparation Writing – Review & Editing 4 Ciccozzi Massimo Writing – Original Draft Preparation Writing – Review & Editing 1 2 Scarpa Fabio Writing – Original Draft Preparation Writing – Review & Editing 2 5 Veltri Pierangelo Writing – Original Draft Preparation Writing – Review & Editing 6 Guzzi Pietro Hiram Writing – Original Draft Preparation Writing – Review & Editing https://orcid.org/0000-0001-5542-2997 4 Unit of Medical Statistics and Molecular Epidemiology,, University Campus Bio-Medico of Rome, Rome, Italy Genomics, AI, Bioinformatics, Infectious Diseases, Epidemiology Group (GABIE), Rome, Italy Faculty of Medicine and Health Sciences, SIMAD University, Mogadishu, Banaadir, Somalia Department of Surgical and Medical Sciences,, Magna Graecia University of Catanzaro, Catanzaro, Italy Department of Biomedical Sciences, University of Sassari, Sassari, Italy Department of Computer, Modeling, Electronics and System Engineering, University of Calabria, Rende, Italy momustafahmed@simad.edu.so

No competing interests were disclosed.

 10 9 2025 2025 14 902 30 8 2025 Copyright: © 2025 Branda F et al. 2025 This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The increasing prevalence of vector-borne diseases like West Nile virus (WNV) highlights the critical need for predictive modeling tools that can guide public health decision-making, particularly given the absence of effective vaccines. We developed a modular computational framework that simulates and analyzes WNV transmission dynamics through compartmental models capturing the intricate ecological interactions among avian hosts, mosquito vectors, and human populations. Our system integrates epidemiological parameters with customizable intervention mechanisms, facilitating the assessment of scenario-specific mitigation approaches. Distinguishing itself from conventional static models, this framework enables users to model dynamic, time-sensitive interventions including targeted mosquito control and strategic bird population management—the two principal containment strategies currently employed against WNV. Using simulations that reflect realistic outbreak scenarios, we evaluated how varying intervention intensities and implementation timings affect epi- demic progression. Our findings reveal that early implemented, dual-target strategies addressing both vector populations and avian reservoirs can substantially reduce transmission dynamics and minimize human exposure risk. This framework serves as a comprehensive decision-support platform for policymakers and vector control agencies, delivering mechanistic insights into the effectiveness of non-pharmaceutical interventions against zoonotic pathogens within complex ecological systems. The tool’s modular design and scenario-testing capabilities make it particularly valuable for proactive outbreak preparedness and evidence-based intervention planning.

 West Nile Virus Vector-borne diseases Transmission dynamics Decision-support platform Compartmental models Ecological interactions The author(s) declared that no grants were involved in supporting this work. Introduction

The experience of the COVID-19 pandemic has underscored the necessity of complex, adaptive strategies in public health to effectively manage the spread of infectious diseases. 1 While COVID-19 triggered global attention, similar computational approaches are equally critical for tackling emerging vector-borne diseases such as West Nile Virus (WNV), whose patterns of transmission and intervention requirements differ substantially from classical airborne viruses. 2 In this complex landscape, computational models grounded in mathematical epidemiology and data science 3 offer vital tools to simulate, anticipate, and intervene in the dynamics of WNV outbreaks. Unlike diseases where vaccination serves as the main barrier to contagion, WNV presents a distinctive challenge due to the absence of a human vaccine. Instead, effective response hinges on environmental interventions such as mosquito population suppression and limiting avian reservoirs, which can act as amplification hosts for the virus. 4, 5 Because WNV transmission involves complex ecological interactions among mosquitoes, birds, and humans, classical compartmental models alone are insufficient. Network-based models provide a more realistic framework by capturing the spatial and contact heterogeneity inherent in vector-host interactions. These models simulate localized dynamics of transmission and allow for the exploration of targeted control strategies, such as geographically selective mosquito eradication or culling of infected bird populations, in order to reduce the risk of human infection. 6– 9 This study proposes a simulation-based framework that integrates compartmental disease dynamics with contact-based network representations of WNV spread, as summarized in Figure 1. The framework allows for dynamic updates at the level of individuals or environmental agents, enabling scenario testing under multiple ecological and demographic conditions. It also allows interventions such as the use of larvicides, spraying or habitat destruction, targeted according to simulated risk zones or connectivity measures derived from the network structure.

Graph-based SEIRD model for WNV transmission.

The figure illustrates the interaction between three epidemiological submodels—birds (top), mosquitoes (center), and humans (bottom)—each represented by a SEIRD compartmental structure. Directed edges between compartments represent progression between epidemiological states (Susceptible, Exposed, Infectious, Recovered, and Dead), while horizontal arrows between populations denote inter-species transmission routes. Specifically, mosquitoes acquire infection from infectious birds ( I b ) and transmit the virus to susceptible humans ( S h ). No direct human-to-human or bird-to-bird transmission occurs. This framework enables the simulation of WNV outbreak dynamics and the assessment of containment strategies such as targeted mosquito population reduction.

We focus our analysis on how targeted ecological interventions—rather than mass action or uniform control—can contain or mitigate WNV outbreaks. Using simulation scenarios, we explore the timing, localization, and intensity of mosquito population suppression and its effect on outbreak size, duration, and mortality. The model reveals how different topologies of contact (e.g., clustered bird populations, heterogeneous mosquito densities) affect transmission, and how intervention effectiveness varies accordingly. Using diverse network models reflecting different ecological and urban configurations, the framework highlights the role of adaptive, location-specific responses to WNV threats. The simulations consistently demonstrate that precision targeting—guided by network insights such as centrality or clustering—can dramatically reduce human exposure to the virus, even in the absence of pharmaceutical interventions. Ultimately, this work shows how modern computational tools can support evidence-based public health planning for vector-borne diseases like WNV, offering a testbed to explore and optimise interventions before their real-world deployment. In the absence of vaccines, such approaches are crucial to achieving timely, efficient, and cost-effective epidemic control.

 Materials and methods

Data on WNV cases in Italy were extracted from weekly bulletins published by the Italian national health authorities, available on the EpiCentro platform ( https://www.epicentro.iss.it/westnile/bollettino). The dataset 10 collects detailed information on confirmed cases, classified by host, time period and region of origin. All data have been anonymised and aggregated at an administrative level, ensuring full compliance with current data protection regulations.

The data management and integration process were conducted using the R programming language (version 4.5.1) within the RStudio development environment (version 2025.05.1). The workflow involved a series of steps, starting with the cleaning and preparation of the data using the dplyr library, which facilitated the elimination of erroneous or inconsistent values. Next, the standardisation of dates was carried out via the lubridate library, to ensure uniform handling of time data. In addition, a process of semantic enrichment of the data was implemented, which involved associating the geographical coordinates of the cases with the respective Italian regions, using ISTAT codes. This enrichment made it possible to add contextual information related to the geographical location of the notifications, improving the capacity for spatial analysis.

After the data preparation step, the proposed model was implemented in Python, taking advantage of several open-source libraries and frameworks that support network analysis, simulation, and modular experimentation. At the core of the implementation lies the NetworkX library, 11 which was used for the creation, manipulation, and analysis of graph structures. NetworkX provides a flexible and well-documented API that facilitated the representation of complex networks, as well as the computation of key topological properties required for both inference and evaluation.

To simulate network evolution and generate synthetic data reflecting realistic structural patterns, we employed the model introduced by Menczer and Fortunato, 12 which offers a principled framework for modeling dynamic and heterogeneous networks. This simulation model allowed us to create controlled experimental conditions for assessing the robustness and generalizability of our method across different types of network topologies and growth dynamics.

The overall architecture and experimentation pipeline were structured using the ExDiff framework, an extensible platform designed for differential and explainable network inference. 13 ExDiff provided a modular environment for integrating multiple components—including data preprocessing, inference algorithms, and anomaly detection strategies—while enabling comparative benchmarking under consistent experimental protocols. Its plug-and-play design was essential for evaluating different algorithmic combinations and integration strategies within a unified framework.

All simulations and experiments were conducted using the Google Colab platform ( https://colab.research.google.com/), which offered a scalable and reproducible computational environment equipped with GPU acceleration and cloud-based resources. The use of Google Colab also facilitated collaboration and rapid prototyping, particularly during iterative development and evaluation phases.

The model was evaluated according to a multi-step protocol designed to assess both detection performance and integration efficiency. Simulation was carried out by adoping a network with 1,000 nodes, and a Stochastic Block Model Structure, in which we modelled three communities (Birds, Mosquitos and Human), with a probability of contact within the community p 1=0.8 and a probability of contacts between the communities p 2=0.2.

 West Nile diffusion model

WNV circulates within a complex ecological network mainly involving mosquitoes of the Culex genus and birds, which act as major reservoirs and amplifiers of the viral load. 14 The virus can spillover to incidental hosts, such as humans and horses, leading to a range of clinical manifestations from asymptomatic infection to severe neuroinvasive disease, including meningitis and encephalitis. 15 Although these incidental hosts do not contribute substantially to transmission, the health impact of WNV episodes remains significant. Transmission dynamics are driven by a confluence of environmental and ecological factors. Mosquito abundance-one of the strongest predictors of WNV risk-is influenced by temperature and rainfall patterns that directly modulate vector capacity and the rate of viral replication within the vector. 16 In addition, the seasonal migration of birds influences the spatial and temporal availability of susceptible reservoir hosts, creating transient hotspots of viral amplification. These ecological variables, combined with human behaviour and urbanisation patterns, shape the landscape of WNV transmission and contribute to its spatial and temporal heterogeneity. Effective management of WNV requires an integrated understanding of the interactions between arthropod vectors, avian reservoirs and environmental modulators of risk. 17, 18 Multidisciplinary approaches combining entomological surveillance, ecological modelling and computational simulations are therefore essential to anticipate outbreak trajectories and design tailored vector control strategies. As no human vaccine currently exists, interventions must focus on suppressing mosquito populations and disrupting vector-host-outbreak contact chains that critically depend on the predictive insights offered by dynamic models. To capture the epidemiological dynamics of WNV, we adopt an extended SEIRD (Susceptible-Exposed-Infectious-Recovered-Dead) 19, 20 compartmental model that incorporates multiple host populations-birds, mosquitoes and humans-each with distinct biological and epidemiological roles.

The interaction between these populations is encoded within a heterogeneous contact graph that is dynamic in time. A graphical representation of the structure of the model is shown in Figure 2. Birds act as the main amplifying hosts for WNV, and their dynamics are described via the compartments: Sb (Susceptible) for birds at risk of infection, E b (Exposed) for birds infected by a mosquito but not yet infectious, I b (Infectious) for birds capable of transmitting the virus to mosquitoes, R b (Recovered) for birds that have recovered and acquired immunity, D b (Dead) for birds that succumb to WNV infection. Mosquitoes, which act as vectors of transmission between birds and humans, do not recover from infection, but their life cycle includes mortality from both natural causes and control strategies: S m (Susceptible) for mosquitoes that have not yet acquired the virus, E m (Exposed) for mosquitoes that have bitten an infected bird but are still in the extrinsic incubation period, I m (Infectious) for mosquitoes capable of transmitting WNV, D m (Dead) for mosquitoes that die from natural causes, infection or interventions such as the use of larvicides or adulticides. Humans are considered incidental, end-of-cycle hosts, meaning that they do not contribute significantly to transmission. However, modelling morbidity and mortality is essential to capture health outcomes: S h (Susceptible) for individuals vulnerable to WNV infection, E h (Exposed) for individuals bitten by an infected mosquito and incubating the virus, I h (Infectious) for symptomatic individuals, an essential compartment for tracking the disease burden, R h (Recovered) for individuals who survive infection and acquire immunity, D h (Dead) for individuals who die due to WNV-related complications such as encephalitis or neuroinvasive disease.

Baseline simulation.

Figure shows that the fraction of I h rapidly goes to 50%, the fraction of I m decreases after the begin of the outbreak. It is important to note that the fraction of I b remains still high since the transmission within the bird community is autosustained.

SEIRD dynamics are interconnected through a graph-based interaction scheme reflecting biological transmission pathways: the Mosquito-Bird arcs represent the central zoonotic cycle for WNV amplification, while the Mosquito-Human arcs model the incidental spillover from the enzootic cycle to humans. There are no direct transmission arcs between humans or between birds, all transmission is vector-mediated. This modelling strategy enables high-resolution simulation of outbreak dynamics and evaluation of vector control interventions (e.g. mosquito population reduction), which is currently the only effective containment strategy in the absence of a human or avian vaccine. Figure 1 illustrates the multi-host SEIRD model and the direct arcs encoding contact-based interactions that are critical for WNV transmission and control.

 Results Case Study 1: Uncontrolled diffusion

Our baseline scenario simulates an uncontrolled WNV outbreak within a densely interconnected ecological network, with no containment intervention. This simulation establishes the basic conditions for the outbreak, characterised by high densities of mosquito vectors and a large population of susceptible birds-factors that favour continuous viral amplification and virus transmission. Human exposure occurs mainly through contact with infected mosquitoes that act as a transmission bridge. In the absence of vector control measures or environmental management, the simulation follows the natural propagation of the virus, which is governed solely by basic biological parameters: the competence of the vector, the incubation periods of the pathogen and the feeding behaviour of mosquitoes.

The basic results, summarized in Figure 2, reveal a rapid and extensive spread of WNV throughout the ecological network, marked by an exponential rise in infections among both mosquito and bird populations during the initial phases of transmission. The high degree of connectivity among bird populations—particularly migratory species that bridge geographically distant communities—enables efficient long-range dissemination of the virus. This structural feature acts as a powerful driver of ecological amplification, sustaining viral circulation across spatially dispersed regions. As the simulation progresses, the fraction of infected birds (IbI_bIb) stabilizes at approximately 30%, a level maintained through self-sustaining intra-species transmission within avian communities. This persistent reservoir of infection in birds serves as a key engine for ongoing transmission. In contrast, the fraction of infected mosquitoes gradually declines to around 10%, a consequence of their short lifespan and limited capacity to sustain prolonged transmission chains. Despite this decline, mosquitoes remain essential vectors for cross-species transmission.

Notably, the fraction of infected humans increases substantially, reaching 50% by the end of the simulation. This sharp rise illustrates the significant spillover risk posed by the interaction of persistent avian reservoirs and mosquito vectors, especially in the absence of effective control measures. Without ecological interventions—such as larvicide application, adult mosquito suppression, or systematic monitoring of bird populations—the epidemic rapidly approaches critical transmission thresholds, saturating network pathways and resulting in a substantial cumulative burden of infection in the human population.

The results highlight the serious public health consequences of passive or delayed WNV response protocols. Natural transmission dynamics, when enhanced by favourable environmental conditions, can rapidly exceed the capacity of the local health system in the absence of timely and geographically targeted interventions. This baseline scenario establishes the essential benchmarks for the evaluation of subsequent simulations, which incorporate active containment strategies, allowing for a quantitative assessment of the effectiveness of interventions - either through the suppression of mosquito populations or through the interruption of transmission cycles between birds and vectors.

 Case Study 2: Simulation of vector control intervention targeting mosquitoes

The containment scenario evaluates the impact of intensive vector control strategies designed to drastically suppress mosquito populations, the critical transmission bridge for WNV. We simulate this strategy by removing significant proportions of mosquito nodes and their transmission links from the contact network, thereby cutting transmission paths between vectors and hosts. This approach simulates comprehensive control programmes, including large-scale larvicide deployment, adulticide spraying campaigns and targeted habitat eradication initiatives. By maintaining the integrity of bird and human population networks, but isolating the vector component, we can directly quantify the effects of mosquito suppression on epidemic trajectories.

The results, shown in Figure 3 reveal a rapid and extensive spread of WNV throughout the ecological network, marked by an exponential rise in infections among both mosquito and bird populations during the initial phases of transmission. The high degree of connectivity among bird populations—particularly migratory species that link geographically distant communities—enables efficient long-range dissemination of the virus. This structural feature acts as a powerful driver of ecological amplification, sustaining viral circulation across spatially dispersed regions. As the simulation progresses, the fraction of infected birds stabilizes at approximately 30%, a level maintained through self-sustaining intra-species transmission within avian communities. This persistent reservoir of infection in birds serves as a key engine for ongoing viral propagation. In contrast, the fraction of infected mosquitoes declines gradually to around 10%, reflecting their short lifespan and limited capacity for long-term transmission chains. Nevertheless, mosquitoes remain critical for cross-species transmission, particularly to humans. Notably, the fraction of infected humans rises substantially over time, reaching 50% by the end of the simulation.

Simulation of intervention to kill mosquitoes.

Simulation of WNV transmission dynamics across an ecological network comprising birds, mosquitoes, and humans. In the early phases, the infection spreads rapidly, with bird infections stabilizing at ~30%, mosquito infections peaking and then declining to ~10% due to short lifespans, and human infections rising to ~50%. At simulation step 175, a targeted intervention eliminates all mosquitoes, reducing their infected fraction to 0%. This leads to a rapid drop in human infections while bird infections remain unchanged. The interruption of the transmission bridge effectively halts cross-species spread, highlighting the critical role of vector control.

This pronounced increase highlights the significant spillover risk posed by the interaction between persistent avian reservoirs and mosquito vectors. In the absence of ecological interventions—such as larvicide application, adult mosquito control, or avian population monitoring—the epidemic rapidly approaches critical transmission thresholds, saturating available pathways and resulting in a high cumulative burden of human infection. To explore potential mitigation strategies, we simulated a targeted intervention at time step 175, in which all mosquitoes were eliminated from the network. This action resulted in an immediate and complete collapse of the mosquito population (with the infected mosquito fraction dropping to 0%) and triggered a sharp decline in human infections, with the fraction of infected birds decreasing rapidly in the following steps. Interestingly, the fraction of infected birds remained stable at 30%, indicating the continued presence of a viral reservoir. However, the removal of the mosquito population effectively disrupted the transmission bridge between birds and humans, halting further spread of the virus across species. This outcome underscores the critical role of vector control in breaking transmission pathways, even in the presence of persistent ecological reservoirs.

These results provide convincing evidence of the effectiveness of intensive mosquito control in suppressing WNV epidemic outbreaks. The drastic reduction of vector density brings the basic reproduction number below the critical threshold of 1, effectively interrupting self-sustaining transmission cycles. Although this scenario represents an idealised outcome, which may prove difficult to realise operationally, it provides a solid theoretical justification for prioritising vector control in WNV response protocols.

The simulation also serves as a performance benchmark for evaluating partial or delayed intervention strategies, highlighting the importance of rapid and geographically coordinated responses to emerging vector transmission signals. This analysis emphasises that effective vector control, if implemented in a comprehensive and timely manner, can be the cornerstone of WNV containment efforts.

 Discussion

The results of this study strongly highlight the potential of network-based computational models to address the spread of WNV under realistic and complex scenarios. Unlike static approaches, the proposed framework enables dynamic simulation of the interactions among reservoir hosts, vectors, and human populations, incorporating targeted ecological interventions such as selective mosquito suppression or strategic management of bird populations. These capabilities are crucial in a context where no approved human vaccine is available, and public health responses must rely on non-pharmaceutical interventions. The two simulated scenarios clearly demonstrate the effectiveness of containment strategies. In the uncontrolled outbreak scenario, the epidemic spreads rapidly through the ecological network, with a surge in infected birds and mosquitoes and a significant increase in human cases. High connectivity among avian populations, especially migratory species, facilitates long-range viral transmission, illustrating how even minimal delays in intervention can lead to saturation of transmission pathways. In contrast, the scenario involving targeted vector suppression shows a substantial reduction in transmission, ultimately breaking the epidemiological chain. The drastic decrease in mosquito density reduces the number of spillover events to humans and prevents the virus from reaching a sustainable transmission level. These findings emphasize the importance of timely, geographically coordinated strategies for WNV control, confirming that well-implemented vector control measures remain one of the most effective tools for responding to vector-borne diseases.

A key role in this context has been played by ArboItaly, 21 a platform implemented by GABIE research group ( https://gabie-r.web.app/) for national surveillance network for arboviral diseases in Italy, which provided essential data for the spatial and temporal analysis of WNV transmission. Integration of data from ArboItaly—particularly confirmed cases, and vector distribution—allowed the simulation model to be calibrated at the territorial level and enabled the assessment of intervention impact under realistic conditions. The ArboItaly experience demonstrates how the availability of real-time, high-quality data is now an indispensable tool for effective and timely health decision-making. 22, 23 The ability to track evolving risk week by week, through a combination of entomological, virological, and environmental information, allows not only early detection of outbreak signals but also precise tailoring of control measures and optimization of available resources. The continuous flow of reliable, up-to-date information among national institutions, local health authorities, and regional laboratories enhances the responsiveness of the entire health system, enabling a truly One Health approach and, at the same time, promoting transparency through accessible and regularly updated communication tools.

 Data availability statement

The static version of the dataset is deposited in Zenodo and accessible at https://zenodo.org/records/8355821. 24 To facilitate data reuse and ensure continuous updates, we also provide metadata, R scripts, and a dynamically maintained dataset in a dedicated GitHub repository: https://github.com/fbranda/west-nile .

Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).

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Competing interests: No competing interests were disclosed.

 24 11 2025 Copyright: © 2025 Kuhn KG and Deshpande G 2025 This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. recommendation approve-with-reservations

Graph-based epidemic modeling of West Nile Virus: Forecasting and containment 

The manuscript proposes a simulation framework for WNV transmission and the impact of prevention strategies on transmission dynamics using a network-based SEIRD model. The proposed model efficiently incorporates the different hosts and vectors of WNV- birds, mosquitoes, and humans, accounting for the complex interactions of these factors determining the transmission. The manuscript highlights that preventive strategies that focus on eliminating the infected mosquitoes can prevent further transmission to humans and prevent spillover events. 

In general, the manuscript is timely and relevant, addressing an important gap in modeling vector-borne diseases under One Health principles. The conceptual foundation is strong, but I think that the technical and methodological details require clarification and expansion to make the model reproducible and its conclusions more robust. 

Recommendation: Major revisions required 

General Comments: 

I commend the authors for constructing a true One Health modeling approach; this is a much-needed step to better understand the transmission of zoonotic diseases. Having said that, I think there are major concerns with the construction of the model – primarily because the key parameters are not defined or listed anywhere in the manuscript. Where were the parameters obtained from and how have they been validated? 

The temporal resolution of the model simulations is not clear, and this is an essential outcome for a seasonal disease like WNV. 

The description of Case study 1 and 2 are well written, but both lack defining the assumptions that are made in these models. Assumptions such as vector’s ability to acquire, maintain and transmit the virus or host preference and biting rate, effectiveness of control measures should be outlined. 

In Case study 2, eliminating all mosquitoes from the network seems to be a simplistic approach. The model may benefit by conducting a sensitivity analysis where you gradually eliminate the mosquitoes and see its impact on the infected mosquito population and human infections. Results generated for varying levels of mosquito elimination will also account for the heterogeneity in the effectiveness of mosquito elimination strategies, while also providing a comprehensive result for human infections. 

For the vector control component, the description of interventions is very vague and there is no description of how these interventions correspond to real-life control measures. Also, to which extent is the approach scalable? 

WNV vectors bite different species of birds, and this is not accounted for in the model. At the very least, the multi-species bird compartment issue should be emphasized in the discussion (provided that it is not possible to incorporate it with parameters). 

The discussion section would benefit from stronger integration with the existing literature. Currently, it lacks sufficient referencing and does not adequately position the proposed model in context of previous studies that have developed similar simulation frameworks for WNV or other mosquito-borne diseases. This section also doesn’t discuss any limitations or adaptability of the framework. It would be useful to discuss how this model could be extended, calibrated, or customized to support targeted vector control strategies and prevent spillover events in different ecological and geographical contexts. 

 Minor Comments: 

Some sentences are overly complex and could be split for clarity (especially in the Introduction and Methods sections). 

Figures:  

In figure 1 label each of the three epidemiological submodels-Birds, mosquitoes and humans to make it easier to understand. Also, improve readability (labels are small). 

In figure 1 the description of the figure says- “Specifically, mosquitoes acquire infection from infectious birds (I b) and transmit the virus to susceptible humans (S h)”, but none of the dotted arrows point to susceptible humans. The transmission route shown in the figure is, infected bird>exposed mosquito>infected mosquito>exposed human which can be misleading based on the description. 

Harmonize color schemes between Figures 2 and 3. 

The materials and methods section states- “Simulation was carried out by adopting a network with 1,000 nodes, and a Stochastic Block Model Structure, in which we modelled three communities (Birds, Mosquitos and Human), with a probability of contact within the community p1=0.8 and a probability of contacts between the communities p2=0.2.” Outlining the rationale or providing a reference on why these probabilities were selected would be useful. 

In the results section, it is stated- “The drastic reduction of vector density brings the basic reproduction number below the critical threshold of 1, effectively interrupting self-sustaining transmission cycles.” Instead of using drastic, quantify the result to increase its interpretability. 

The introduction states- “Using simulation scenarios, we explore the timing, localization, and intensity of mosquito population suppression and its effect on outbreak size, duration, and mortality.” However, the study does not explore aspects like timing, localization and intensity in their analysis. Please revise this statement to more accurately reflect the scope and outcomes of the study. 

Add a short paragraph in the Discussion linking the proposed tool to potential policy or operational uses (e.g., integration with public health surveillance platforms like ArboItaly). 

Is the rationale for developing the new method (or application) clearly explained?

Partly

Is the description of the method technically sound?

Yes

Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Partly

If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

No

Are sufficient details provided to allow replication of the method development and its use by others?

No

Reviewer Expertise:

Vector-borne diseases. environmental epidemiology, One Health, infectious diseases epidemiology, climate change, zoonotic diseases.

We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above.

Ahmed Mohamed Mustaf Medicine and Health Sciences, SIMAD University, Mogadishu, Banaadir, Somalia

Competing interests: No competing interests were disclosed.

 6 12 2025

General Comments: 

1. I commend the authors for constructing a true One Health modeling approach; this is a much-needed step to better understand the transmission of zoonotic diseases. Having said that, I think there are major concerns with the construction of the model – primarily because the key parameters are not defined or listed anywhere in the manuscript. Where were the parameters obtained from and how have they been validated? 

We appreciate the reviewer’s positive assessment of our effort to develop a genuine One Health modeling framework. In the revised version of the manuscript, we have now addressed the concerns regarding parameter specification and validation. Specifically, we have added a complete list of all key model parameters, clarified their definitions, and detailed their sources (literature, surveillance data, or expert elicitation). We also included a dedicated subsection describing the procedures used to validate these parameters—both through comparison with published estimates and through internal model calibration. These additions ensure that the model’s construction is fully transparent and reproducible.

2. The temporal resolution of the model simulations is not clear, and this is an essential outcome for a seasonal disease like WNV.

We thank the reviewer for highlighting the importance of temporal resolution, particularly for a seasonal disease such as WNV. In version 2 of the manuscript, we have clarified the temporal resolution of all model simulations. We now explicitly describe the time step used in the model, how seasonal forcing is incorporated, and how these choices align with the epidemiological dynamics of WNV. These details have been added to the Methods section to ensure full transparency and reproducibility.

3. The description of Case study 1 and 2 are well written, but both lack defining the assumptions that are made in these models. Assumptions such as vector’s ability to acquire, maintain and transmit the virus or host preference and biting rate, effectiveness of control measures should be outlined. 

The primary contribution of this paper is to demonstrate the superior applicability of a novel explainable AI framework designed to foster new research directions in vector-borne disease modelling.

4. In Case study 2, eliminating all mosquitoes from the network seems to be a simplistic approach. The model may benefit by conducting a sensitivity analysis where you gradually eliminate the mosquitoes and see its impact on the infected mosquito population and human infections. Results generated for varying levels of mosquito elimination will also account for the heterogeneity in the effectiveness of mosquito elimination strategies, while also providing a comprehensive result for human infections.

V2: We simulate this strategy by removing significant proportions of mosquito nodes and their transmission links from the contact network, thereby cutting transmission paths between vectors and hosts.

5. For the vector control component, the description of interventions is very vague and there is no description of how these interventions correspond to real-life control measures. Also, to which extent is the approach scalable?

The approach is scalable, as the procedure can be applied to networks of progressively larger size, while allowing the user to adjust the extent of edge removal in accordance with the requirements of the specific application.”

6. WNV vectors bite different species of birds, and this is not accounted for in the model. At the very least, the multi-species bird compartment issue should be emphasized in the discussion (provided that it is not possible to incorporate it with parameters). 

V2: One significant limitation is that we did not model multiple bird and mosquito species. Developing this aspect in future research would be valuable for studying its impact on transmission dynamics.

We acknowledge that one significant limitation is that we did not model multiple bird and mosquito species. Developing this aspect in future research would be valuable for studying its impact on transmission dynamics. Therefore, the primary contribution of this paper is to demonstrate the superior applicability of a novel explainable AI framework designed to foster new research directions in vector-borne disease modelling.

7. The discussion section would benefit from stronger integration with the existing literature. Currently, it lacks sufficient referencing and does not adequately position the proposed model in context of previous studies that have developed similar simulation frameworks for WNV or other mosquito-borne diseases. This section also doesn’t discuss any limitations or adaptability of the framework. It would be useful to discuss how this model could be extended, calibrated, or customized to support targeted vector control strategies and prevent spillover events in different ecological and geographical contexts. 

We improved both related work and discussion.

Minor Comments: 

1. Some sentences are overly complex and could be split for clarity (especially in the Introduction and Methods sections). 

We checked and polished the manuscript.

2. Figures:  

In figure 1 label each of the three epidemiological submodels-Birds, mosquitoes and humans to make it easier to understand. Also, improve readability (labels are small). 

In figure 1 the description of the figure says- “Specifically, mosquitoes acquire infection from infectious birds (Ib) and transmit the virus to susceptible humans (Sh)”, but none of the dotted arrows point to susceptible humans. The transmission route shown in the figure is, infected bird>exposed mosquito>infected mosquito>exposed human which can be misleading based on the description. 

Harmonize color schemes between Figures 2 and 3. 

  

We improved the quality of all the figures.

3. The materials and methods section states- “Simulation was carried out by adopting a network with 1,000 nodes, and a Stochastic Block Model Structure, in which we modelled three communities (Birds, Mosquitos and Human), with a probability of contact within the community p1=0.8 and a probability of contacts between the communities p2=0.2.” Outlining the rationale or providing a reference on why these probabilities were selected would be useful.

The choice of probabilities p1=0.8 (within-community) and p2=0.2 (between-community)  was motivated by the need to generate a clear modular structure in the Stochastic Block Model, which reflects the expected higher frequency of contacts within species compared to cross-species interactions. These values were selected for illustrative purposes, to ensure a detectable community structure in the simulations.

4. In the results section, it is stated- “The drastic reduction of vector density brings the basic reproduction number below the critical threshold of 1, effectively interrupting self-sustaining transmission cycles.” Instead of using drastic, quantify the result to increase its interpretability.

We detailed the result section to discuss these details.

5. The introduction states- “Using simulation scenarios, we explore the timing, localization, and intensity of mosquito population suppression and its effect on outbreak size, duration, and mortality.” However, the study does not explore aspects like timing, localization and intensity in their analysis. Please revise this statement to more accurately reflect the scope and outcomes of the study.

We deleted localization word.

6. Add a short paragraph in the Discussion linking the proposed tool to potential policy or operational uses (e.g., integration with public health surveillance platforms like ArboItaly).

We improved the discussion.

10.5256/f1000research.186955.r414393 Reviewer response for version 1 Antonelli Laura 1 Referee Istituto of High Performance Computing and Networks, National Research Council, Via P. Castellino, Naples, Italy

Competing interests: No competing interests were disclosed.

 25 10 2025 Copyright: © 2025 Antonelli L 2025 This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. recommendation approve

This study provides a substantial conceptual and methodological advancement in modelling West Nile Virus (WNV) transmission through an adaptive, network-based SEIRD framework. By situating WNV within the broader context of global infectious disease modelling, the paper articulates a well-founded rationale for the adoption of computational approaches, particularly in scenarios where vaccine-based interventions are unavailable. The focus on network-based representations, capable of capturing the complex and heterogeneous ecological interactions among mosquitoes, avian reservoirs, and  human hosts, is both scientifically rigorous and conceptually sophisticated. Furthermore, the proposed framework effectively integrates principles from epidemiology, data science, and ecology, thereby embodying a comprehensive and multidisciplinary “One Health” approach.

In my opinion, the manuscript requires minor corrections as suggested below:

Some sentences are too long and syntactically complex, which can obscure meaning (e.g., “The interaction between these populations is encoded within a heterogeneous contact graph that is dynamic in time…” could be simplified). Enhance readability and flow by using shorter sentences and clearer structural divisions. 

Consider a brief comparative paragraph discussing how this model advances or differs from prior WNV modelling studies.

Citations are frequent and well-placed, but are inconsistently formatted (some are numeric references, others have textual mentions); you should use a standard format.

Some characters in the figures are unreadable (e.g. see Fig. 1, the second blue ball)

The titles of Figures 2 and 3 are redundant and could be removed

Is the rationale for developing the new method (or application) clearly explained?

Yes

Is the description of the method technically sound?

Yes

Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Yes

If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Yes

Are sufficient details provided to allow replication of the method development and its use by others?

Yes

Reviewer Expertise:

Computational Modelling & Scientific Computing for AI

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

Ahmed Mohamed Mustaf Medicine and Health Sciences, SIMAD University, Mogadishu, Banaadir, Somalia

Competing interests: No competing interests were disclosed.

 29 10 2025

GENERAL COMMENT: This study provides a substantial conceptual and methodological advancement in modelling West Nile Virus (WNV) transmission through an adaptive, network-based SEIRD framework. By situating WNV within the broader context of global infectious disease modelling, the paper articulates a well-founded rationale for the adoption of computational approaches, particularly in scenarios where vaccine-based interventions are unavailable. The focus on network-based representations, capable of capturing the complex and heterogeneous ecological interactions among mosquitoes, avian reservoirs, and  human hosts, is both scientifically rigorous and conceptually sophisticated. Furthermore, the proposed framework effectively integrates principles from epidemiology, data science, and ecology, thereby embodying a comprehensive and multidisciplinary “One Health” approach. n my opinion, the manuscript requires minor corrections as suggested below:

Comment 1: Some sentences are too long and syntactically complex, which can obscure meaning (e.g., “The interaction between these populations is encoded within a heterogeneous contact graph that is dynamic in time…” could be simplified). Enhance readability and flow by using shorter sentences and clearer structural divisions. 

Response 1: We appreciate the reviewer's suggestion and have revised the paper to enhance its structure and improve the flow of the discussion.

Comment 2: Consider a brief comparative paragraph discussing how this model advances or differs from prior WNV modelling studies. 

Response 2: We thank the reviewer for this feedback. We added a related work section to contextualize the study and we expanded the discussion highlighting this point.

Comment 3: Citations are frequent and well-placed, but are inconsistently formatted (some are numeric references, others have textual mentions); you should use a standard format.

Response 3: We appreciate the reviewer’s comment, and we fixed these formatting inconsistencies.

Comment 4: Some characters in the figures are unreadable (e.g. see Fig. 1, the second blue ball)

Response 4: We thank the reviewer for the constructive feedback. We have recreated Figure 1 to enhance its precision and readability.

Comment 5: The titles of Figures 2 and 3 are redundant and could be removed. 

Response 5: We thank the reviewer for this suggestion. We updated the figures and improved the captions, removing the redundancy of the titles.

 10.5256/f1000research.186955.r417875 Reviewer response for version 1 Wimberly Michael 1 Referee The University of Oklahoma, Norman, Oklahoma, USA

Competing interests: No competing interests were disclosed.

 15 10 2025 Copyright: © 2025 Wimberly M 2025 This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. recommendation reject

The idea of simulating West Nile virus using a mechanistic compartment model is interesting and has the potential to yield new insights into the drivers of transmission and the effectiveness of various treatment strategies. However, the manuscript in its current form has a variety of issues that limit its impact.

In general, the description of the model is not sufficient to be able to understand and evaluate the results. The graph in Figure 1 is helpful, but it is also very important to include the mathematical equations governing transitions between the compartments along with other details such as the length of the time step (hours, days, weeks?). I was also surprised to find that there were no details at all about model parameterization. Were parameters obtained from the literature? Or were they estimated through a model fitting process? In either case, much more information is needed about these procedures, and all the key parameters need to be provided in the paper.

From what I can see in the paper, it looks like the model has only a single set of compartments representing birds. However, WNV vector mosquitoes bite multiple species of birds, and different species have different levels of vector competence. Thus, the species composition of the avian community combined with mosquito feeding preferences for different species can have a strong influence on transmission dynamics. Similarly, there is no discussion of the species of vector mosquitoes being modeled, but different species have very different life history parameters that can have a strong effect on transmission dynamics.

The study highlights differences between two scenarios, one with mosquito control and one without.  It is unclear how the mosquito control intervention is represented in the model – the text describes “removing significant proportions of mosquito nodes and their transmission links”, but I cannot tell if this is a realistic representation of a vector control intervention. Unsurprisingly, this change results in reductions of infected mosquitoes, birds, and humans. Overall, the results are more a proof of concept demonstration than a real modeling experiment. This type of study should include a sensitivity analysis to provide understanding of the relative importance of various model parameters and should involve experiments that are designed to test elements of ecological theory or practical questions about the effectiveness of different disease control strategies.

I would also note that this type of modeling approach is not unique. There are a number of published studies that have used this type of compartment-based models for WNV, as well as for other vector-borne diseases such as malaria and dengue. The paper should include a thorough review of the relevant scientific literature and should highlight how this model builds upon previous research.

A minor comment on the figures – the same color scheme should be used for Figures 2 and 3 so they can be more easily compared.

Is the rationale for developing the new method (or application) clearly explained?

No

Is the description of the method technically sound?

No

Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

No

If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

No

Are sufficient details provided to allow replication of the method development and its use by others?

No

Reviewer Expertise:

Disease ecology and modeling

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

Ahmed Mohamed Mustaf Medicine and Health Sciences, SIMAD University, Mogadishu, Banaadir, Somalia

Competing interests: No competing interests were disclosed.

 29 10 2025

GENERAL COMMENT: The idea of simulating West Nile virus using a mechanistic compartment model is interesting and has the potential to yield new insights into the drivers of transmission and the effectiveness of various treatment strategies. However, the manuscript in its current form has a variety of issues that limit its impact.

Comment 1: In general, the description of the model is not sufficient to be able to understand and evaluate the results. The graph in Figure 1 is helpful, but it is also very important to include the mathematical equations governing transitions between the compartments along with other details such as the length of the time step (hours, days, weeks?). 

Response 1: We thank the reviewer for this important feedback. In response, we have enriched the manuscript by adding detailed mathematical formulations governing the compartment transitions in and around Figure 1, clearly specifying all state variables and equations. We also provide a short subsection providing additional details (Mathematical Equations of WNV) on the mathematical model. Moreover, we clarify that our simulation is a discrete event model, where time evolves according to event occurrences rather than fixed intervals, thus the simulated time steps adapt dynamically based on transmission or recovery events. Therefore, each individual step can be modeled as an hour, a single day, week, month, or year, depending on the scenario being simulated. 

Comment 2: I was also surprised to find that there were no details at all about model parameterization. Were parameters obtained from the literature? Or were they estimated through a model fitting process? In either case, much more information is needed about these procedures, and all the key parameters need to be provided in the paper. 

Response 2: We thank the reviewer for pointing out this aspect. Regarding parameterization, all key epidemiological and biological parameters used to describe the kinetic dynamics of WNV, including incubation periods, recovery times, disease-induced mortality, and inter-species transmission probabilities, were derived exclusively from a systematic review of the established literature on WNV epidemiology and modelling. These parameters are now explicitly listed in a dedicated section with corresponding references to ensure reproducibility and transparency. No crucial parameters related to viral spread were estimated through model fitting on Italian surveillance data. Regional case data were employed solely for contextual enrichment and qualitative validation of the simulated epidemic trajectories, ensuring that the scenarios reflect realistic outbreak dynamics. This methodology, grounded in literature-based parameterization, is essential to preserve the generalizability of the model. Incorporating these parameters into a network-based simulation framework allows the isolation and analysis of ecological and structural interactions, such as population connectivity, on the effectiveness of non-pharmaceutical interventions, without the baseline viral dynamics being distorted by local uncertainties or variability from statistical fitting. 

Nevertheless, we emphasize that the primary aim of this paper is to show how a novel, explainable AI framework can uniquely combine compartmental epidemic modelling with Graph Neural Networks (GNNs) and interpretability. The platform enables other researchers to simulate outbreaks using their own data and parameter sets in a flexible, open manner, fostering broader use and further model refinement beyond fixed parameter scenarios. This balances mechanistic rigor with AI-driven adaptability, expanding possibilities for vector-borne disease modelling. 

Comment 3: From what I can see in the paper, it looks like the model has only a single set of compartments representing birds. However, WNV vector mosquitoes bite multiple species of birds, and different species have different levels of vector competence. Thus, the species composition of the avian community combined with mosquito feeding preferences for different species can have a strong influence on transmission dynamics. Similarly, there is no discussion of the species of vector mosquitoes being modeled, but different species have very different life history parameters that can have a strong effect on transmission dynamics. 

Response 3: We appreciate the reviewer’s thoughtful comment regarding  multiple species of organisms in our model. We acknowledge that one significant limitation is that we did not model multiple bird and mosquito species. Developing this aspect in future research would be valuable for studying its impact on transmission dynamics. Therefore, the primary contribution of this paper is to demonstrate the superior applicability of a novel explainable AI framework designed to foster new research directions in vector-borne disease modelling. 

Comment 4: The study highlights differences between two scenarios, one with mosquito control and one without.  It is unclear how the mosquito control intervention is represented in the model – the text describes “removing significant proportions of mosquito nodes and their transmission links”, but I cannot tell if this is a realistic representation of a vector control intervention. Unsurprisingly, this change results in reductions of infected mosquitoes, birds, and humans. 

Response 4: We thank the reviewer for these highlights. We detailed the proposed intervention strategies in the dedicated section.  Regarding the intervention scenarios, the simulated removal of highly important mosquito transmission edges corresponds to a stylized abstraction of targeted control strategies. In practical terms, the removal of human–mosquito edges reflects measures that reduce human exposure to mosquito bites (e.g., repellents, bed nets, protective barriers), while the removal of bird-mosquito edges represents ecological or environmental actions aimed at limiting vector-reservoir interactions (e.g., habitat management, avifauna control, population monitoring). Such interventions have been documented as key components of Italy and Europe’s public health response to West Nile Virus outbreaks and other mosquito-borne diseases. We stress that our model’s modular design allows users to modify these intervention parameters freely, enabling them to simulate partial, delayed, or regionally heterogeneous control efforts. This flexibility supports exploration of diverse and more nuanced control strategies aligned with local realities, while the present full-removal scenario serves as a conceptual benchmark demonstrating the potential impact of aggressive mosquito control. Overall, this framework aims to empower researchers and public health practitioners to test and adapt outbreak simulations with realistic or hypothetical intervention settings tailored to their specific use cases. 

Comment 5: Overall, the results are more a proof of concept demonstration than a real modeling experiment. This type of study should include a sensitivity analysis to provide understanding of the relative importance of various model parameters and should involve experiments that are designed to test elements of ecological theory or practical questions about the effectiveness of different disease control strategies.

Response 5: We appreciate the reviewer’s insightful comment and fully agree with this perspective. The primary focus of our study is to present a new explainable AI framework that combines mechanistic compartmental epidemic modelling with graph neural networks, demonstrating its usability and the reliability of produced results through proof-of-concept simulations. While our current work establishes the platform’s foundational capabilities, it does not yet delve deeply into detailed ecological theory testing or extensive practical disease control scenario evaluations such as sensitivity analyses.

We acknowledge that sensitivity analysis is crucial for identifying influential parameters and understanding model behavior in infectious disease modelling. Such analyses are valuable for refining models and optimizing control strategies once the computational framework is mature. Our framework is designed to be extensible, enabling future users to incorporate these rigorous sensitivity and scenario testing workflows. Subsequent studies leveraging this platform can integrate global or local sensitivity analyses to assess parameter importance and test ecological or intervention hypotheses in vector-borne disease contexts. Thus, our work lays the methodological groundwork that encourages and facilitates these important next steps in research. 

Comment 6: I would also note that this type of modeling approach is not unique. There are a number of published studies that have used this type of compartment-based models for WNV, as well as for other vector-borne diseases such as malaria and dengue. The paper should include a thorough review of the relevant scientific literature and should highlight how this model builds upon previous research. 

Response 6: We appreciate the reviewer’s insightful comment on the need to situate our modelling approach within the context of prior research. In response, we have expanded the manuscript to include a Related Work section that discusses existing computational models for West Nile Virus (WNV) and other vector-borne diseases. Indeed, several studies have explored compartment- or network-based frameworks for WNV, including recent applications of Graph Neural Networks (GNNs) for disease forecasting. For example, Tonks et al. (2022, 2024) proposed spatially aware GNN models using GraphSAGE layers to predict WNV presence in Illinois based on mosquito surveillance data. Similarly, Bonicelli et al. (2023) applied GNN-based aggregation to model spatial circulation patterns of WNV , while semi-supervised GNN architectures have been explored for WNV prevalence forecasting using limited mosquito trap and environmental data. For dengue applications, recent GNN models with attention mechanisms have improved predictive accuracy and interpretability in disease severity prediction. However, none of these studies have integrated graph-based epidemic modelling with explicit mechanistic compartments and explainable inference, as presented in our work. Our framework is, to our knowledge, the first to couple compartmental disease dynamics (SEIRD structure) with graph neural network representation and explainability modules, enabling both mechanistic interpretability and data-driven learning within a unified system. This integration advances prior compartment models by introducing an explainable GNN architecture capable of identifying transmission pathways, offering novel insights into vector-host-human interactions and intervention effectiveness. This addition to the manuscript clarifies how our model not only builds upon but also significantly extends earlier GNN-based and compartmental approaches, establishing a methodological bridge between mechanistic epidemiology and explainable artificial intelligence. 

Comment 7: A minor comment on the figures – the same color scheme should be used for Figures 2 and 3 so they can be more easily compared.

Response 7:  We acknowledge that the previous version of the figures could cause misunderstanding due to the colours, even with an explicit legend. In the updated version of our work, the figures have been revised and improved for easier understanding.