I think I now understand the problem identified in my previous post, at least partially. Looking at the section "Make the susceptible neighbors of infected agents meet their neighbors" in the efficient method, and in particular the line Flatten[Lookup[neighbors,Normal[stateAgents["I"]]],1], this picks out all agents that are connected to an infected agent. However, in cases where an agent is connected to more than one infected agent they are then double-counted, effectively being given more than one opportunity to be infected in a single step (note that the fact that they are more likely to be infected if they are connected to more than one infected agent is already taken account of elsewhere).

A simple fix is to change the line to DeleteDuplicates[Flatten[Lookup[neighbors,Normal[stateAgents["I"]]],1]]. This significantly improves the agreement with the slower implementation, although there is still some discrepancy, with the efficient method now slightly favoring a later and lower peak.

Aristeidis, I can give you a rough benchmark: I use a desktop with Xeon E2176M 6 core + 16GB RAM to run the whole notebook. It consumes 10 GB (maximum resource I have besides OS resources) and takes 3655 seconds to complete (using ParallelTable). Attached is a notebook with only input code from Christopher's article and my timing result.

Attachments:

covid.nb

Thanks for this very interesting post.

I did some experiments with your two different implementations and found that they behave differently in a statistically significant sense. To verify this, I ran your simple example a large number of times (1000 simulations) using both implementations and extracted the time and magnitude of the infection peak. The attached histograms show the results. Orange is the "Efficient implementation" and blue is the other implementation. You can see that the infection peak is earlier and higher when run with the efficient implementation, suggesting that it has a higher effective transmission rate.

I thought I understood both implementations, but there must be something I am missing as I can't see why they should behave differently. Can anyone explain why I am finding differences?

Excellent post @Christopher Wolfram , I was working along the same lines. I'll switch the focus to cover other interesting aspects of using this type of models.

Dear Christopher, Thank you for your prompt reply! I believe I did not run out of memory. I am trying again, using ParallelTable.

Does this model enable to evaluate a number of infected people, using very long tail(s) of the confirmed cases (for example, using published data from China)? My thought was - the number of reported can be lower than the real/infected cases, but to make a justified decision on quarantine stop, one has to know both.

Ah, that's a good catch. I'll try to add that change to the notebook and edit the post.

Great, thank you for checking.

Do you understand why the two implementations might still differ? They are in much closer agreement now, but there still seems to be a small, but statistically significant difference (as measured by, e.g. the time and height of the peak infection).

Dear Christopher,

Congratulations on the development of a very useful contagion network model. I have been working along the same issues using production networks (in which economic shocks are considered as disease propagation), which are structurally different from your contagion model based on undirected graphs. I have changed few properties of your model to experiment with directed production graphs.

My question: except a change in "agentNeighborhood" code to "Catenate[{#1 -> #2}", is there any other place that needs to be adjusted to accommodate directed networks? If so, could you please let me know which parts of your code needs revising to also study shock propagation in directed networks?

Furthermore, reading the comments on your code, I wonder whether there is a fundamental difference between simple and efficient implementations. I thought they would both produce the same results, but apparently experiments by others in this forum indicate that they are different in several respects like peak infection and speed of infection. Am I right?

Look forward to hearing from you.

Tugrul Temel