Analysis of Epidemic Models in Complex Networks and Node Isolation Strategie Proposal for Reducing Virus Propagation

Round 1

Reviewer 1 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

The paper in question appears to delve into the intricate dynamics of virus propagation in computer networks, taking inspiration from mathematical models typically employed in epidemiology, such as SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-Removed), and SIRS (Susceptible-Infected-Removed-Susceptible). The authors' focal point is the analysis of SIS-type and SIRS-type models, particularly one originally proposed by Chakrabarti and an iteration of the SIRS model developed by the authors.

By conducting simulations, the author examines how network topology influences the spread dynamics of a virus. They discuss the critical role of the largest eigenvalue (λ1) of the adjacency matrix in controlling virus spread, a topic that has been previously established in the literature. The complex problem of minimizing the spectral radius to inhibit virus spread, known as NP-complete, is acknowledged, and heuristic approaches are considered.

The author presents an innovative approach to network protection by transforming any given network topology into an approximately regular topology through edge elimination. This transformation strategy is a practical method to induce rapid virus extinction, even if the resulting topology is not theoretically optimal for limiting virus propagation. The paper compares regular low-degree topologies, like a lattice with degree 4 (Lattice4), against more complex binomial and power-law topologies through simulations, underscoring the effectiveness of the former in virus extinction.

While the paper contributes to the existing body of work on virus propagation in networks, there are some areas where it could potentially fall short:

1. The simulations might benefit from additional validation against real-world virus propagation events, providing stronger support for the model's practical relevance.

2. The comparison between different topologies might be too narrow if the simulation parameters are not diverse enough. It's essential to consider a broad range of network conditions to ensure that the conclusions are robust.

3. While the proposed edge elimination technique is practical, the paper could discuss in greater detail the trade-offs involved, such as the potential impact on network functionality and performance.

4. If heuristic algorithms are suggested for edge elimination, their computational efficiency and scalability should be thoroughly evaluated and compared to existing methods.

5. It should be clear if the findings can be generalized to various types of networks or if they are specific to certain network structures and sizes.

Recommendations:

1. It is recommended to expand the current research analysis, including an overview of viruses spreading in network models, e.g. doi: 10.1615/TelecomRadEng.v78.i5.60 , 10.1016/j.asoc.2020.106784

2. Extend simulations to include various network structures and scenarios, especially those that reflect real-world complexities.

3. Investigate and discuss the potential impacts of the recommended topology transformation on network performance and utility.

4. Incorporate real-world case studies or data to validate the model's predictions and the efficacy of the proposed mitigation strategy.

5. Perform sensitivity analyses to understand how parameter changes affect the model's outcomes, providing insights into the robustness of the proposed strategies.

The article presents a thoughtful exploration of virus spread in computer networks through the lens of epidemic modeling, offering novel insights into the impact of network topology on virus propagation dynamics. The author's proposal to use edge elimination to transform networks into regular topologies is a practical approach that merits consideration, especially in scenarios where rapid virus extinction is paramount.

However, the paper could be strengthened by expanding the breadth of simulations, providing more detailed algorithmic descriptions, assessing broader impacts on network functionality, and by supporting findings with real-world data. The recommendations, if implemented, could significantly enhance the paper's value to the field of network security, providing both theoretical insights and actionable strategies for practitioners.

Author Response

Comments

and

Suggestions

for Authors

The paper in question appears to delve into the intricate dynamics

of virus propagation in computer networks, taking inspiration from

mathematical models typically employed in epidemiology, such as

SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-

Removed), and SIRS (Susceptible-Infected-Removed-

Susceptible). The authors' focal point is the analysis of SIS-type

and SIRS-type models, particularly one originally proposed by

Chakrabarti and an iteration of the SIRS model developed by the

authors.

By conducting simulations, the author examines how network

topology influences the spread dynamics of a virus. They discuss

the critical role of the largest eigenvalue (λ1) of the adjacency

matrix in controlling virus spread, a topic that has been previously

established in the literature. The complex problem of minimizing

the spectral radius to inhibit virus spread, known as NP-complete,

is acknowledged, and heuristic approaches are considered.

The author presents an innovative approach to network protection

by transforming any given network topology into an approximately

regular topology through edge elimination. This transformation

strategy is a practical method to induce rapid virus extinction, even

if the resulting topology is not theoretically optimal for limiting virus

propagation. The paper compares regular low-degree topologies,

like a lattice with degree 4 (Lattice4), against more complex

binomial and power-law topologies through simulations,

underscoring the effectiveness of the former in virus extinction.

While the paper contributes to the existing body of work on virus

propagation in networks, there are some areas where it could

potentially fall short:

1. The simulations might benefit from additional validation against

real-world virus propagation events, providing stronger support for

the model's practical relevance.

 

Answer:

 

In the introductory section of  the article I mentioned that the article is of theoretical carácter.

For this reason no real data are presented. However, it is also worth mentioning that the research presented in the article may have practical applications that could be explored in the future.

 

2. The comparison between different topologies might be too

narrow if the simulation parameters are not diverse enough. It's

essential to consider a broad range of network conditions to ensure

that the conclusions are robust.

 

Answer:

In the article we compare the Powerlaw type topology and the Lattice-4 type topology because the first is dense and the other not so much. To carry out this comparison, the epidemic model is simulated in both topologies under the same conditions (for instance in SIS Chakrabarty model, delta=0.5,gamma=0.3,beta=0.4), that is, with the same values ​​of the parameters of the epidemiological model. Likewise, in order to explore sensitivity, in the simulation some parameters are varied in increments of 0.05 and others are kept constant. This is mentioned in the captions of the figures presented. When doing the simulations, depending on the values ​​of the parameters, the following cases may occur:1) The number of infected nodes was higher than the number of non-infected nodes in the Powerlaw type topology and in the Lattice4 type topology the difference between infected nodes and non-infected nodes was significantly reduced or even the no infected nodes were more than the infected nodes.2) The number of infected nodes was higher than the number of uninfected nodes in the Powerlaw type topology and in the Lattice4 type topology, fast extinction of the virus occurred.In fact, I performed many more simulations with the SIS and SIRS models with different values ​​of delta, gamma, beta , nu, and chi, obtaining the behaviors mentioned above. I did not include these simulations so as not to fill the article with graphs, but I have added in subsection 3.1 of the article, some simulations to illustrate what I am commenting on.

 

3. While the proposed edge elimination technique is practical, the

paper could discuss in greater detail the trade-offs involved, such

as the potential impact on network functionality and performance.

 

Answer:

 

The idea behind isolation strategies is not the efficiency of information transmission but on the contrary, by seeking to reduce the spectral radius of the graph, it is intended that the virus takes longer to spread. This is discussed in subsection 4.1 of the article.In this same subsection it is also commented that the isolation strategy seeks to reduce the connectivity of the network nodes without reaching the extreme case of isolating nodes.

 

 

4. If heuristic algorithms are suggested for edge elimination, their

computational efficiency and scalability should be thoroughly

evaluated and compared to existing methods.

 

 

5. It should be clear if the findings can be generalized to various

types of networks or if they are specific to certain network

structures and sizes.

Recommendations:

 

1. It is recommended to expand the current research analysis,

including an overview of viruses spreading in network models, e.g.

doi: 10.1615/TelecomRadEng.v78.i5.60 ,

10.1016/j.asoc.2020.106784

 

Answer:

Thank you for the recommendation. I already  downloaded and started Reading the articles. The first is related with network security and the second article is related with simulation of virus propagation with multiagent systems using Netlogo. Three years ago I have implemented some simulations of virus propagation using Netlogo.

 

2. Extend simulations to include various network structures and

scenarios, especially those that reflect real-world complexities.

 

Answer:

 

As I commented in one of the previous answers, in subsection 4.1, I added some additional simulations. To write the article I also carried out simulations of other topologies such as Binomial or Exponential and the behavior was similar to that of the Powerlaw type networks, that is why I did not add them to the article.

 

 

 

 

3. Investigate and discuss the potential impacts of the

recommended topology transformation on network performance

and utility.

 

Answer:

The idea behind isolation strategies is not the efficiency of information transmission but on the contrary, by seeking to reduce the spectral radius of the graph, it is intended that the virus takes longer to spread. This is discussed in subsection 4.1 of the article. The utility of the isolation strategy that I proposed is to reduce the propagation of the virus in a less extreme way that the total isolation of the network nodes.

 

4. Incorporate real-world case studies or data to validate the

model's predictions and the efficacy of the proposed mitigation

strategy.

 

Answer:

 

The article is theoretical in nature. However, in future articles I will try to deal with case studies with real data in order to contrast my strategy with real cases.

 

 

5. Perform sensitivity analyses to understand how parameter

changes affect the model's outcomes, providing insights into the

robustness of the proposed strategies.

The article presents a thoughtful exploration of virus spread in

computer networks through the lens of epidemic modeling, offering

novel insights into the impact of network topology on virus

propagation dynamics. The author's proposal to use edge

elimination to transform networks into regular topologies is a

practical approach that merits consideration, especially in

scenarios where rapid virus extinction is paramount.

However, the paper could be strengthened by expanding the

breadth of simulations, providing more detailed algorithmic

descriptions, assessing broader impacts on network functionality,

and by supporting findings with real-world data. The

recommendations, if implemented, could significantly enhance the

paper's value to the field of network security, providing both

theoretical insights and actionable strategies for practitioners.

 

Answer:

I already added some simulations in the subsection 4.1. Thank you very much for your comments and recomendations.

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The authors studied some epidemic model in complex networks and investigate the conditions under which a virus becomes rapidly extinct in the network. The work is interesting and I suggest the following improvements:

1- The computational cost and execution time of numerical simulations can be elaborated.

2- It may be better to compare the results with some realistic data.

3- What are the advantages of employing discrete-time models rather than the conventional continuous-time ones?

4- What are the effects of heterogeneity in degrees of the nodes on the obtained results

Author Response

Comments

and

Suggestions

for Authors

The authors studied some epidemic model in complex networks

and investigate the conditions under which a virus becomes rapidly

extinct in the network. The work is interesting and I suggest the

following improvements:

 

1- The computational cost and execution time of numerical

simulations can be elaborated.

 

Answer:

I added  the subsection 3.2 Time Complexity of the Simulations in the new versión of the article.

 

2- It may be better to compare the results with some realistic data.

Answer:

 

 In the introductory section of the article I mentioned that the article is of theoretical kind.

For this reason no real data are presented. However, it is also worth mentioning that the research presented in the article may have practical applications that could be explored in the future.

 

3- What are the advantages of employing discrete-time models

rather than the conventional continuous-time ones?

 

Answer:

As I mention in subsection 3.1 Discret SIS and SIRS epidemic models, I assume that the discrete time steps tend to 0, which makes the results also apply to the continuous case. On the other hand, the discrete model allows expressions of said model to be expressed by a recurrence which is easy to evaluate and program through iterations.

 

 

4- What are the effects of heterogeneity in degrees of the nodes on

the obtained results

Answer:

Topologies with heterogeneity in the degrees of the nodes are related to topologies that appear in complex networks such as Powerlaw and these structures have some properties such as the formation of giant components or small-world properties. These characteristics of Powerlaw topologies mean that information spreads quickly or that even though some edges disappear randomly, the graph remains connected. In the case of virus propagation, these types of topologies are adverse because the virus spreads very quickly.

 

Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

See the attached report

Comments for author File: Comments.pdf

Comments on the Quality of English Language

See the attached report

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

The authors have addressed reviewers' recommendations. The paper can be accepted.

Author Response

Thank you very much

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The manuscript can be accepted in its present form.

Author Response

Thank you very much

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

I see that you have taken into account my comments.

There is a minor probem with my comment 16. I have wrongly written "Shoudn't you rather consider more sets of parameters ?" In fact what I meant is "Shoudn't you rather consider a larger set of values of the three parameters?". Of course I do not suggest to add new parameters. But I do not understand why you don't increase independenty the values of the three parameters. Why add the increment Delta simultaneously to the three parameters ? Can you consider this point ?

Author Response

In this version of the article, in order to meet the request to
add additional simulations where the behavior of the model would
be shown by varying a single parameter at a time,
figures 24,25,26,27,28 and 29 were added.
This simulations were added at the end of the section
3.1. Discrete SIS and SIRS Epidemic Models

Round 3

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Thank you for the additional simulations.

Maybe you could add some comment on what they reveal.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1) The author formulated "hints for the health administration to prevent the infection, the pandemic..." as the goal of this paper. But I don't see clear recommendations.

2) Some network topologies are presented, but it is not clear which of them should be used.

3) The meaning of the "vector field" in the figs. 3, 9, 11, 12, 14, 15 is not obvious for me, please clarify

4) It seems to me as a review paper to overview some classical models (SIR, SIS) and network based models, but there are a lot of english language mistakes and it's complicated to understand what the author wants to say.

5) In the attached file there are some marked comments and points which should be modified.

6) A comparison of the model results with real data would be interesting. If this is not possible the author must remark that the examples are theoretical ones only.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

see the comments above

Reviewer 2 Report

Comments and Suggestions for Authors

The paper primarily focuses on analyzing the influence of network topology on virus propagation dynamics, drawing inspiration from various epidemiological models such as SIS, SIR, and SEIR. The article aims to understand how modifications in the original network can offer effective isolation strategies to reduce the spread of viruses in computer networks. The paper also draws parallels between the development of mathematical models in the field of virus spread in computer networks and epidemiology.

Strengths:

1. The paper provides a comprehensive historical account of mathematical models used for studying epidemic processes, establishing a foundation for the context of the study.
2. Recognizing the influence of network topology on virus propagation dynamics can be valuable for computer network administrators and epidemiologists.
3. Bridging computer science and epidemiology, the paper offers insights into how concerns in one field can contribute ideas to the other.

Drawbacks:

1. While the paper mentions analyzing "a particular model proposed in the past", there is no clear indication of which model this refers to. This omission may need to be clarified with the subject.
2. The abstract and conclusion do not hint at any empirical or quantitative findings. Readers might benefit from a clearer indication of the results.
3. Some sentences are lengthy, making it challenging to discern the main points. For example, the closing section of the abstract could be split into multiple sentences for clarity.

Recommendations:

1. It is vital to present data in an easily digestible format. Graphs, tables, and charts can help readers understand the impact of network topology on virus propagation.
2. Breaking down complex sentences and avoiding jargon can enhance readability and make the paper more accessible to a broader audience.
3. Since isolation strategies are a key takeaway, it would be beneficial to delve deeper into specific strategies and their potential impacts.
4. Including a few case studies showing the application of the findings in real-world scenarios might be helpful. This would underline the paper's relevance and importance.
5. Since the paper suggests a potential feedback loop where insights from computer virus spread can aid epidemiological strategies, this area could be expanded upon to show concrete examples or suggestions.
6. The figures should be presented as graphs, not as a screenshot.
7. The conclusions should be expanded with concrete outcomes of the study.
8. The current research analysis section should be included.
9. Including the discussion section is recommended.

The paper presents an intriguing intersection of computer networks and epidemiology, attempting to bridge the gap between two seemingly distinct fields. While the foundation is solid, improvements in clarity, specificity, and presentation of findings can significantly enhance the paper's value and relevance.