City Transmission Networks: Unraveling Disease Spread Dynamics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Summary of Review

·        The manuscript presents a comprehensive and novel approach to analyzing disease spread using city transmission networks. The methodology is robust, and the results provide valuable insights into the dynamics of COVID-19 transmission in Saudi Arabia. The paper is well organized and will be a valuable addition to the relevant literature after several modifications.

·        Though the use of a network-based model is well designed and executed there are a few methodological details that could use further clarification. Please provide more details on the data cleaning steps employed and the criteria for inclusion and/or exclusion. Furthermore, clarify the choosing of epidemiological and structural metrics in the network analysis. These specifics will allow others to repeat your methods.

·        I am a little confused by Figure 3 and the degree difference. Please expand on this and what it means.

·        Please consider more discussion on the potential impact of travel restrictions and lockdowns in relation to your findings. This could also tie into a sensitivity analysis. I am not suggesting doing a sensitivity analysis but you could strengthen your findings by expounding on these effects on the model.

·        Also, you need to further elaborate on when a city is determined to be “infected” I cannot make that out. Is a city “infected” if it has a single case of disease? Does it need to reach a level of infection before you consider the city ”infected”. This could have important ramifications to your findings. Please further describe this.

·        At line 46 and 47 “It allows us to assess the role of different cities in the spread of a disease and identify 46 potential superspreaders, who are individuals who disproportionately contribute to the 47 transmission of infectious diseases by infecting a large number of susceptible contacts [22],” here you are jumping to different scales and it is confusing. This is not a model of individual transmission and here you identify a superspreader as an individual that spreads the disease by higher mobility. So you are looking for superspreader cities. I would clarify this more succinctly.

·        In your discussion and conclusion “Our analysis indicates that finding superspreader cities is more important than identifying viral sources.” This is too much of a blanket term. You might say something like, “Our analysis indicates finding superspreader cities is more important, in the early stages of an epidemic/pandemic, than tracing the route of community–level disease transmission.” This would make sense too, right? But does this also suggest the major importance of your modeling is its ability to detect superspreader cities?

 

·        Emphasize the unique advantages of the network-based approach in identifying superspreader cities based on connectivity rather than just population size. We would expect a city with more edges to be more likely to be a superspreader so underscore the value of the network-based approach to other types of epidemiological analyses. i.e population-based approaches sans networks. Also, in the discussion, discuss how the network-based approach provides additional insights into disease spread dynamics that are not captured by alternative methods.

Comments on the Quality of English Language

• Ensure consistent formatting of in-text citations and references.
  
  
• Minor grammatical corrections are needed (e.g., "each node pair" should be "each pair of nodes").

Author Response

Point 1.1: Please provide more details on the data cleaning steps employed and the criteria for inclusion and/or exclusion.

Response 1.1: To address this concern, we implemented the following steps:

• We documented the total number of records before and after dataset cleaning (lines 282-283 and lines 292-2893):
• “The dataset was procured from the Saudi Ministry of Health [26], covering the period from March 2, 2020, to April 25, 2020, and consisting of 198,018 records.”
• “After applying these cleaning steps, the dataset was reduced to 1,366 records.”

 

• We provided a clear explanation for each exclusion criterion (lines 289-293):
• First, we excluded any records that indicated a negative or not confirmed COVID-19 outcome, ensuring that our dataset focused exclusively on confirmed cases.
• Second, records of individuals who tested positive for COVID-19 but had no travel history were excluded. This step ensured that the analysis concentrated on cities with initial imported cases.

 

Point 1.2: clarify the choosing of epidemiological and structural metrics in the network analysis. These specifics will allow others to repeat your methods.

Response 1.2: As suggested by the reviewer, we clarified the selection of epidemiological and structural measures by adding an explanation in the introduction of Subsection 4.2 (lines 204-211):

 

“Epidemiological measures are used to assess the evolving epidemiology of a disease. These metrics are crucial for understanding how infections propagate between nodes within the network, highlighting key transmission paths and the overall reach of the disease. Structural measures focus on the overall topology and connectivity of the epidemic network. These metrics are important for understanding the static properties of the network that might impact disease propagation. They provide insights into the network’s connectivity, and the hierarchical organization of infected nodes.”

 

Additionaly, we provided a detailed explanation of each measure after its definition. Impcated lines: 220-222, 226-227, 232-233, 238-239, 242-243, and 250.

 

Point 1.3: I am a little confused by Figure 3 and the degree difference. Please expand on this and what it means.

Response 1.3: Figure 3 is presented in Subsection 5.3.1 (Global Properties of Transmission Network), where it serves to outline the basic properties of the COVID-19 transmission network. The figure is intended to give the reader an initial understanding of the network's structure, setting the stage for more detailed epidemiological and structural analyses discussed later, such as the Measure Degree Center in Subsection 5.3.3 (Structural Properties of Transmission Networks). To clarify any potential confusion and provide additional insights, we have included the following enhancements in Subsection 5.3.1 (lines 339-342):

“The degree distribution depicted in Figure 3 highlights a skewed pattern, with most nodes having a low out-degree and a few nodes exhibiting higher connectivity. This heterogeneity indicates that certain cities play disproportionately influential roles in disease transmission, acting as hubs in the network.”

Point 1.4: Please consider more discussion on the potential impact of travel restrictions and lockdowns in relation to your findings. This could also tie into a sensitivity analysis. I am not suggesting doing a sensitivity analysis but you could strengthen your findings by expounding on these effects on the model.

Response 1.4: Following the reviewer's suggestion, we have expanded Subsection 5.4 (Discussion) to include a detailed analysis of the potential impacts of travel restrictions and lockdowns in light of our findings (lines 464-470):

 

“Consequently, authorities should prioritize enforcing lockdowns in these cities to effectively mitigate the spread of the disease. By focusing preventative measures and resources on Arriyad and Makkah, where the transmission dynamics have demonstrated a central role in the network, targeted interventions can be more strategically implemented. This approach not only curtails the further spread of the virus from these hubs but also allows for a more efficient allocation of healthcare resources and public health responses, potentially leading to a quicker containment of the outbreak.”

 

Point 1.5: you need to further elaborate on when a city is determined to be “infected” I cannot make that out. Is a city “infected” if it has a single case of disease? Does it need to reach a level of infection before you consider the city ”infected”. This could have important ramifications to your findings. Please further describe this.

Response 1.5: We added a clarification for this concern in Subsection 4.1 (Transmission Network Construction) as follows (lines 187-191):

 

“All central nodes are considered infected because they host at least one individual who contracted the disease while travelling. The remaining cities become infected when a person in that city is confirmed to have the disease. Each of these cities is linked to another city from which they contracted the disease and to another city to which they transmitted the infection”

 

 

Point 1.6: At line 46 and 47 “It allows us to assess the role of different cities in the spread of a disease and identify potential superspreaders, who are individuals who disproportionately contribute to the transmission of infectious diseases by infecting a large number of susceptible contacts [22],” here you are jumping to different scales and it is confusing. This is not a model of individual transmission and here you identify a superspreader as an individual that spreads the disease by higher mobility. So you are looking for superspreader cities. I would clarify this more succinctly.

Response 1.6: We understand that adding indivudals to the definition of “superspreaders” add condusion. Therefore, as suggested by the reviewer, we clarified that the intended meaning behind “superspreaders” is cities and not individuals as follows (lines 48-51):

 

“It allows us to assess the role of different cities in the spread of a disease and identify potential superspreaders (cities with the highest potential to disseminate the disease). This highlights the critical importance of managing these influential nodes in disease control efforts.”

 

The list of references has been updated accordingly.

 

Point 1.7: In your discussion and conclusion “Our analysis indicates that finding superspreader cities is more important than identifying viral sources.” This is too much of a blanket term. You might say something like, “Our analysis indicates finding superspreader cities is more important, in the early stages of an epidemic/pandemic, than tracing the route of community–level disease transmission.” This would make sense too, right? But does this also suggest the major importance of your modeling is its ability to detect superspreader cities?

Response 1.7: We have updated the Conclusion section in accordance with the reviewer's suggestion (lines 498-501).

 

“Our analysis suggests that identifying superspreader cities is crucial in the early stages of an epidemic, more so than community-level disease transmission. This is because the effects of infections in these cities are not confined to local boundaries but can extend across regional borders, impacting neighboring areas.”

 

Point 1.8: Emphasize the unique advantages of the network-based approach in identifying superspreader cities based on connectivity rather than just population size. We would expect a city with more edges to be more likely to be a superspreader so underscore the value of the network-based approach to other types of epidemiological analyses. i.e population-based approaches sans networks.

Response 1.8: We have revised the Introduction to emphasize the significance of utilizing network-based models focused on connectivity rather than solely relying on population size as follows (lines 58-61):

 

“Our approach emphasizes city connectivity over population size when studying disease propagation, recognizing that population size alone has limitations as a reliable predictor of disease spread”

 

Point 1.9: Also, in the discussion, discuss how the network-based approach provides additional insights into disease spread dynamics that are not captured by alternative methods.

Response 1.9: We have updated the Discussion section in accordance with the reviewer’s suggestion (lines 446-452).

 

“Network-based approaches provide additional insights into disease spread dynamics that are not captured by alternative methods. Unlike traditional models, network-based approaches can incorporate more information and handle complex interactions between geographical locations. This level of information richness offers a better representation of disease transmission through specific pathways and superspreader cities. The network-based method improves epidemic forecasting accuracy while also providing actionable information for more effective disease control and prevention strategies.”

 

Point 1.10: Ensure consistent formatting of in-text citations and references.

Response 1.10: The text has been revised and updated as suggested.

 

Point 1.11: Minor grammatical corrections are needed (e.g., "each node pair" should be "each pair of nodes").

Response 1.11: The text has been revised and updated as suggested.

 

 

 

 

 

 

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The article is a comprehensive study aimed at understanding the dynamics of disease transmission by constructing and analyzing city transmission networks. The research focuses on using network-based epidemic models to identify the roles cities play in the spread of diseases, with the primary objective of pinpointing superspreaders. The writing is relatively complete, and the thinking is clear, the analysis methods in the article are quite innovative. There is the following suggestion or question:

(1) What does “disproportionately contribute to” mean in “individuals who disproportionately contribute to the transmission of infectious diseases by infecting a large number of susceptible contacts”.

(2) What is the difference between “accessibility” and “reachability”?

(3) I think the role of BFS and node centrality measures in this paper and their relation to "the possibility of infection" should be explained in section 2.

(4) Section 3 is too lengthy. It can be shorter by reducing some examples.

(5) Section 4.1 should include a diagram to illustrate your study area or the network you have constructed.

(6) What does “The network is undirected but directed to delineate the flow of transmission” mean?

Author Response

Point 2.1: What does “disproportionately contribute to” mean in “individuals who disproportionately contribute to the transmission of infectious diseases by infecting a large number of susceptible contacts”.

Response 2.1: The definition of “superspreaders” has been updated to clarify any confusion as follows (lines 48-51):

“It allows us to assess the role of different cities in the spread of a disease and identify potential superspreaders (cities with the highest potential to disseminate the disease). This highlights the critical importance of managing these influential nodes in disease control efforts”

 

The list of references has been updated accordingly.

 

 

Point 2.2: What is the difference between “accessibility” and “reachability”?

Response 2.2: Accessibility often focuses on the immediate environment of a node (local perspective), while reachability considers the entire network (global perspective). To clarify this distinction, we provided explanations for each concept as follows (lines 73-75):

 

“A crucial role in disease transmission is played by node accessibility (the local environment of the node) and reachability (the global environment of the node) within network structures”

 

Point 2.3:  I think the role of BFS and node centrality measures in this paper and their relation to "the possibility of infection" should be explained in section 2.

 

Response 2.3: We have updated the Prelimenary section in accordance with the reviewer’s suggestion (lines 104-119).

 

“This systematic exploration helps in visualizing the spread and reach of potential infections across the network.

Node centrality measures rank nodes with respect to their importance by assigning a numerical value to each node according to its location in the network, which influences the overall dynamics of network interactions. Degree centrality considers the central nodes as those with the highest number of connections, highlighting potential hubs of activity or transmission. Closeness centrality identifies the center of the network as the subset of nodes with the shortest average distance to all other nodes, thereby highlighting those that can most efficiently spread or gather information, or, in the context of epidemics, transmit infections. In tree-structured networks, closeness centrality offers profound insights; the center, often referred to as the median and typically consisting of one or two nodes, is deemed the pivotal point of the network. This designation underscores its importance in strategic interventions and control measures. The application of closeness centrality is crucial for identifying key nodes, which are prioritized for thorough analysis and targeted in preventive strategies within epidemiological studies. This approach ensures that efforts are concentrated where they can be most effective in mitigating the spread of disease.”

 

Point 2.4:  Section 3 is too lengthy. It can be shorter by reducing some examples.

Response 2.4: We have updated Section 3 (Related Work) in accordance with the reviewer's suggestion.

 

Point 2.5: Section 4.1 should include a diagram to illustrate your study area or the network you have constructed.

Response 2.5: Section 4.1 introduces the method used to construct the transmission network. Our constructed network is then detailed in Section 5 (Illustrative Example). We added a sentence to Section 4.1 to reference the example in Figure 1, as follows (lines 197-198):

 

"See Figure 1 for an example of a transmission network."

 

The caption of Figure 1 has been updated accordingly.

 

Point 2.6: What does “The network is undirected but directed to delineate the flow of transmission” mean?

Response 2.6: We revised the sentence in Subsection 4.1 to remove any ambiguity. The new sentence now reads as follows (lines: 196-197):

 

“The resulting network is undirected; however, we use directed edges to emphasize the chronological flow of disease transmission.”

 

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This is an interesting mathematical model (or rather series of models) for city-to-city disease transmission, using Covid-19 and cities in Saudi Arabia as a demonstration. Overall the manuscript is well written and the methods appear sound. The following comments should therefore be considered relatively minor criticisms/concerns.

The framing of the study as seeking to identify superspreaders is at times a little confusing. Superspreaders are generally individuals, as you describe on lines 19 and 47. Your analysis is focused on cities, and you sometimes use the term "superspreader cities" (lines 61, 469, 490, etc.), but other uses of the superspreader term (lines 417, 460, 467) are less clear. Are these individuals or cities? I worry the concept of a superspreader may not translate well to the scale of an entire city, and perhaps a different term would be more appropriate. 

A related concern is how the individual-level Covid data were converted to city-scale data. After re-reading section 5.1 I remain confused about how this aggregation/conversion took place. If the scale of the analysis is cities and regions, did you need to remove records lacking travel history? I'm not saying these should be put back in, I'm merely expressing my confusion as to why they were left out - it was not clear to me from the manuscript what the rationale was.

In a few places, including the Conclusion, you suggest these models could be used to help target quarantine/lockdowns or otherwise improve disease control efforts. As written this feels like a stretch to me - could you perhaps include a specific example of how these tools could be used? For example, if these models were being developed in near-real-time during the early months of the pandemic, would they have identified Arriyad or Makkah as key locations in time for control efforts to be put in place, or do these models rely on the full time series in order to effectively identify tree structure? Another example might be preventative - can these models help Saudi officials prioritize stockpiling of supplies in specific regions/cities? If so, where? If these models are not capable of supporting such recommendations, perhaps you could describe the necessary next steps or improvements to get to that level?

Comments on the Quality of English Language

Minor typos and grammatical errors throughout. A few examples provided:

Line 134 - "Furhtermore" should be Furthermore

Line 158 - "in in"

Line 232 - "The network is undirected but directed ..." It is possible this is the correct way to describe such a network, but it sounds like a contradiction. 

Line 338 - "thighs" should be ties and "arbitrary" should be arbitrarily

Author Response

Point 3.1: The framing of the study as seeking to identify superspreaders is at times a little confusing. Superspreaders are generally individuals, as you describe on lines 19 and 47. Your analysis is focused on cities, and you sometimes use the term "superspreader cities" (lines 61, 469, 490, etc.), but other uses of the superspreader term (lines 417, 460, 467) are less clear. Are these individuals or cities? I worry the concept of a superspreader may not translate well to the scale of an entire city, and perhaps a different term would be more appropriate.

Response 3.1: We understand the confusion regarding the term "superspreaders." In this context, it refers to cities (hosting infected individuals). We have updated lines 9, 13-14, 442, and 457 to clarify this meaning. While terms like "epicenter city" or "spreader hub" could be used, we believe that "superspreader city" is more intuitive and easier to understand.

 

Additionally, we have added the following sentence to the Introduction to emphasize this connection (lines 23-25):

 

“Interestingly, some cities exhibit characteristics that significantly influence the spread of diseases, similar to the role of individual superspreaders in an outbreak, prompting the adoption of the concept of superspreader cities.”

 

Point 3.2: A related concern is how the individual-level Covid data were converted to city-scale data. After re-reading section 5.1 I remain confused about how this aggregation/conversion took place. If the scale of the analysis is cities and regions, did you need to remove records lacking travel history? I'm not saying these should be put back in, I'm merely expressing my confusion as to why they were left out - it was not clear to me from the manuscript what the rationale was.

Response 3.2: Travel history is crucial for identifying cases that originated from countries where the virus was endemic. Therefore, records of individuals who tested positive for COVID-19 but had no travel history were excluded, as these cases likely represent community transmission rather than imported cases. This decision was made to focus on analyzing the initial importation of the virus in each city (imported cases serve as seed nodes in the transmission process). Subsequent disease spread was obtained from the reported date for each city from the COVID-19 Dashboard: Saudi Arabia (https://covid19.moh.gov.sa/).

To eliminate ambiguity, we have added the following sentence to Section 5.1 (lines 291-293):

“Second, records of individuals who tested positive for COVID-19 but had no travel history were excluded. This step ensured that the analysis concentrated on cities with initial imported cases.”

 

Point 3.3: In a few places, including the Conclusion, you suggest these models could be used to help target quarantine/lockdowns or otherwise improve disease control efforts. As written this feels like a stretch to me - could you perhaps include a specific example of how these tools could be used? For example, if these models were being developed in near-real-time during the early months of the pandemic, would they have identified Arriyad or Makkah as key locations in time for control efforts to be put in place, or do these models rely on the full time series in order to effectively identify tree structure? Another example might be preventative - can these models help Saudi officials prioritize stockpiling of supplies in specific regions/cities? If so, where? If these models are not capable of supporting such recommendations, perhaps you could describe the necessary next steps or improvements to get to that level?

Response 3.3: As recommended by the reviewer, we have included an example of real-time application of the model and a preventative use case in the Discussion section (lines 477-487):

 

“Because the model relies on the daily number of confirmed cases, it enables the real-time identification of critical locations for early intervention with a certain degree of precision. It uses epidemiological metrics, such as the Total Number of Chains at each central node, to decide the role of these nodes in disease spread, even before the pandemic ends and without complete time series data. This capability for early detection could have allowed authorities to implement targeted quarantine measures to effectively mitigate the impact of an outbreak. Furthermore, our model facilitates the efficient allocation and management of healthcare resources, thereby reducing the pressures on national healthcare systems. It empowers authorities to more effectively distribute medical supplies and other essential items to strategically important cities. By preparing essential nodes in the virus propagation network ahead of time, we can ensure better readiness for potential outbreaks.”

 

We also added the following to the Conclusion section (lines 508-510):

 

“Moreover, the model can be applied in real-time to offer insights into the role of cities in disease transmission.”

 

Point 3.4: Minor typos and grammatical errors throughout. A few examples provided:

Response 3.4: As suggested by the reviwer, we thoroughly reviewed the manuscript to correct any grammatical or spelling errors.

 

Point 3.5: Line 232 - "The network is undirected but directed ..." It is possible this is the correct way to describe such a network, but it sounds like a contradiction.

Response 3.5: We revised the sentence in Subsection 4.1 to remove any ambiguity. The new sentence now reads as follows (lines: 196-198):

 

“The resulting network is undirected; however, we use directed edges to emphasize the chronological flow of disease transmission.”

 

 

 

Author Response File: Author Response.docx