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

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.

I made that change and recomputed everything. None of the results look significantly affected, but thanks for finding that bug. The main post has been updated to show results from the new version.

Nice post, Christopher, thanks. It shows the power of Mathematica to generate and manipulate efficiently highly structured systems. We're working on similar structured-contact covid model for local settings (e.g. hospitals, city districts et al). Would be glad to share it, when ready

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

Outstanding post, Christopher!

It's intriguing that the shape of the infected curve in the Simple Example section is fairly symmetrical and does not have the long exponential tail.

Generating the phase plane analysis from the simulations is amazing. I've seen (and done) these analyses using the traditional calculus-based approach, but it's wonderful that you can do the same with this model and show that many of the same principles apply.