Notes on Complex Systems, Part 3
Well, back down the rabbit hole this morning. (Part 1 and Part 2 on complex systems.)
Started looking up gravity models and epidemiology (first here, then here, then here, then eventually here).
A few observations:
One of the starting points for much of this work seems to be with the population. So you're able to model within a given population (defined as existing within a given geographical unit/container/scale) the relationship between four groups (susceptible, latent, infected, removed) [See here for a useful visualization of that relationship based on several parameters]. But the limitation of this model is that it assumes that the relationships between these four groups are mostly endogenous - i.e., confined to interactions within the system. Human life doesn't work like that.
So one of the reasons why some seem to have turned to gravity models is that they seem to provide a model for interaction between different population in two different places. So in its early 1970s form, gravity models seems to be something useful to explain, for example, the number of truck trips between two places. The greater the aggregate volume in each place, for example, the greater total relationship. There's an inverse relationship with distance: The greater the distances involved, the smaller the relationship between those two places. [The friction of distance, again.]
In any event, one of the really humbling things about doing this reading is just the sheer number of variables involved. For example, to think about New York City and possible movement of Covid-19 from New York City to elsewhere. [Where will the disease spread? How quickly will it spread? How will it affect the populations of the places to which it spreads? etc.] So let's say we were working with a matrix that mapped out all of the passenger traffic between New York City and elsewhere. We'd have to cover a range of different forms of transportation: Airlines; trains; personal automobiles; buses; etc. Once we realize that, the actual physical distance doesn't matter as much. Because the geography of this pandemic isn't organized in terms of countries, we need to think about the relative nature of these connections.
Complex systems, indeed.
In any event, I ended up finding my way onto the work of the Global Epidemic and Mobility Project. One of their splash graphics tells us:
It's a really remarkable project - as one of their early papers explains (Balcan et al., Modeling the Spatial Spread of Infectious Diseases), the project is an effort to link agent-based models (basically, how diseases spread within populations; but these models are often limited by the quality of data that goes into them) and large-scale spatial metapopulation models (I think these are what the SEIR models are?). But one question I had: Why frame your project as putting these tools "in the hands of experts"? That's one of the things I've been trying to make sense of - why does model thinking matter in this moment?
***
Balcan et al., Modeling the Spatial Spread of Infectious Diseases. Journal of Computational Science 2010; 1(3):132-145.
Barrios JM, Verstraeten WW, Maes P, Aerts JM, Farifteh J, Coppin P. Using the gravity model to estimate the spatial spread of vector-borne diseases. Int J Environ Res Public Health. 2012;9(12):4346–4364. Published 2012 Nov 30. doi:10.3390/ijerph9124346
Started looking up gravity models and epidemiology (first here, then here, then here, then eventually here).
A few observations:
One of the starting points for much of this work seems to be with the population. So you're able to model within a given population (defined as existing within a given geographical unit/container/scale) the relationship between four groups (susceptible, latent, infected, removed) [See here for a useful visualization of that relationship based on several parameters]. But the limitation of this model is that it assumes that the relationships between these four groups are mostly endogenous - i.e., confined to interactions within the system. Human life doesn't work like that.
So one of the reasons why some seem to have turned to gravity models is that they seem to provide a model for interaction between different population in two different places. So in its early 1970s form, gravity models seems to be something useful to explain, for example, the number of truck trips between two places. The greater the aggregate volume in each place, for example, the greater total relationship. There's an inverse relationship with distance: The greater the distances involved, the smaller the relationship between those two places. [The friction of distance, again.]
In any event, one of the really humbling things about doing this reading is just the sheer number of variables involved. For example, to think about New York City and possible movement of Covid-19 from New York City to elsewhere. [Where will the disease spread? How quickly will it spread? How will it affect the populations of the places to which it spreads? etc.] So let's say we were working with a matrix that mapped out all of the passenger traffic between New York City and elsewhere. We'd have to cover a range of different forms of transportation: Airlines; trains; personal automobiles; buses; etc. Once we realize that, the actual physical distance doesn't matter as much. Because the geography of this pandemic isn't organized in terms of countries, we need to think about the relative nature of these connections.
Complex systems, indeed.
In any event, I ended up finding my way onto the work of the Global Epidemic and Mobility Project. One of their splash graphics tells us:
***
Balcan et al., Modeling the Spatial Spread of Infectious Diseases. Journal of Computational Science 2010; 1(3):132-145.
Barrios JM, Verstraeten WW, Maes P, Aerts JM, Farifteh J, Coppin P. Using the gravity model to estimate the spatial spread of vector-borne diseases. Int J Environ Res Public Health. 2012;9(12):4346–4364. Published 2012 Nov 30. doi:10.3390/ijerph9124346
Grais, R.F., Hugh
Ellis, J. & Glass, G.E. Assessing the impact of airline travel on
the geographic spread of pandemic influenza.
Eur J Epidemiol 18, 1065–1072 (2003). https://doi.org/10.1023/A:1026140019146
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