SIS Epidemic Propagation on Scale-Free Hypernetwork

Round 1

Reviewer 1 Report

 

The authors study the SIS model (2 parameters) of infection spreading on a hypergraph generated as a nontrivial generalization of a simple scale-free network. The implemented dynamic rules use the infection and recovery probabilities that are the same for all nodes within a hyperlink, and both apply at every step. The motivation is to include more complex social connections (micro-communities) captured by hyperlinks beyond standardly used pairwise couplings, e.g. in ref.[7].

Even though the model is still too simple for describing a natural infection process, its simplicity allows for an analytical description (MF limit). Its primary value is that the obtained results override the long prevailing results of ref.[7] based on a simple scale-free network.

 

Even though the manuscript is clearly written, it would benefit from additional rewriting, as explained below, and a reduction of the number of (similar) figures.

For example, Figs.6&7 and Figs.8&9 could be put together as a multi-panel fig.

Figure captions should be more explicit; for example, instead of “Simulation results with …”, one should precisely state what is plotted, for example, ”The simulated density of infected nodes \rho vs time t for different network sizes.” And similarly to other figures.

The term “general complex network” is misleading and wrong. The authors consider “a simple scale-free network” known as BA network. [Please note that BA network does not describe anyone of realistic social structures, which are known to have assortativity, link correlations, higher-order structures such as simplicial complexes, etc., see, for example, “Hierarchical sequencing of online social graph” in Physica A 436, pp. 582-595 (2015) and references there]. Search & Replace “general complex network”-> ”simple scale-free network”. Also, in line 336, replace “informed”->” infected”.

Line 363-364: “Therefore, the hyperlink structure can better reflect the reality…”; No reality data are considered here or reference to such data supporting the observed behavior?

 

In the Introduction, lines 122-123, “their (model)” needs to be clarified. Also, please rephrase the last sentence in the Introduction, lines 131-134, to briefly describe what these new features bring about.  

Moreover, the statement “individual behavior patterns” together with “individual-based modeling” suggests that the network’s nodes (i.e., actors of the infection process) possess individual properties, such as individual susceptibility to the infection considered in the agent-based approach (see “Modeling latent infection transmissions through biosocial stochastic dynamics” PLOS one 15;e0241163 (2020), and “Microscopic dynamic modeling unravels the role of asymptomatic virus carriers in sars-cov-2 epidemics at the interplay of biological and social factors” in Computers in Biol. and Med. 133, 104422 (2021)], which considerably affects the infection spreading. But here, it is only different connectivities.

A discussion would be in order regarding the impact of the higher-order couplings captured by hyperlinks in comparisons with those described by simplicial complexes; in particular, it regards the absence of an abrupt transition of the infection density [see “Abrupt phase transition of epidemic spreading in simplicial complexes”, Phys. Rev Res. 2, 012049 (2020)].

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

The authors present a model based on hypernetworks to study epidemic propagation. The authors applied mean field theory to obtain an analytical expression and compare it with simulations. In the result section they compare the results of hypernetworks with 'general complex networks' - that would be the standard complex network framework.

From the complex networks perspective the article is interesting, hypernetworks have many applications and it is a topic that lacks content. However, I have doubts if the proposed model explores the multi-level properties of the hypernetworks. According with the author's model, there are not so much difference from the hypernetworks, if I am wrong about it, it would be important the authors make the advantages of hypernetwork very clear in text.

I made the simple mental model, if I have 3 nodes, lets say 1, 2 and 3. What is the difference from connecting the node 1 to 2 and 1 to 3, from a hyperlink connecting 1, 2 and 3 simultaneously? I think the hyperlink would be important for the situations where each 'link dimension' would be associated with a different feature. I would like to see a  clarification from the authors about it.

Another important issue from the text is the author's claim that infection spread fast in the hypernetwork. My question on this issue is that it is difficult to compare a standard complex network to a hypernetwork. Would be possible to compare a 1D to a 2D system? I am saying this because I do not think the section 4.2 is a fair comparison.

To sum up, there are two things that I believe require clarification. First, for the proposed model what is the advantage of hypernetwork? Second, besides improving the infection spreading, what is the model advantage in the study of epidemic propagation?

Minor Revisions:

- The font size of the axis labels in the figures should be increased, they are too small.

- The first time BA scale-free model appear in the text Barabasi-Albert should be explicit.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

I am in accordance with the authors reply at points 1, 2 and 3. However, I still think that the community approach could be applied in standard (2D) complex network  without using hypernetworks. Despite of that, which I believe is more a conceptual discussion, I believe the article is suitable for publication based on the fact that it contributes to the discussion about the use of hypernetworks in the study of epidemics. For future publications,  I recommend to the author to provide more details about the advantages of the hypernetworks.

The authors improved the figures, but Figures 5, 6, 8, 9 and 10, are still difficult to read. Maybe the (a) and (b) figures should be adjusted one below the other.

Author Response

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Author Response File: Author Response.docx