[Population Modeling] Description of research

[Nathan Geffen]

Dear all

Jacob has asked me to describe the population modelling work I'm doing with
Stefan.

In simulations of sexually transmitted infections how do we match agents
with each other in sexual partnerships, and how does this affect the
outcomes of simulations? In the simplest differential equation models, it
is implied that all members of the population are equally likely to pair
with each other (see for example perhaps the most cited HIV population --
and maybe any STI  -- model ever, Granich et al 2009
<http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(08)61697-9/fulltext>
which
implicitly makes this assumption - its simplicity is part of its appeal).
This is similar to the simplest simulations where any member of the
population is equally likely to pair with any other. But if we have
information (or assumptions) about who people are actually more likely to
partner with, perhaps this will give us more accurate or realistic models
and better insights into how infections spread.

The problem can be stated like this: given a set of agents, each
representing a person or animal seeking a (sexual) partnership, find a set
of partnerships such that every agent is paired with one and only one other
agent. We need this assumption too: for any two agents a and b we have a
distance function that calculates how realistic it is that a and b can
become sexual partners. This distance function creates an ordering such
that for any two potential partners, b and c, of a, we can calculate
whether b or c is the more likely partner (perhaps with some arbitrary
tie-breaking method). For example, the distance function might calculate
that a 25 year-old heterosexual male living in Berlin is more likely to
partner with a 25-year-old heterosexual female living in Berlin than a 45
year-old gay male living in Munich. but the latter in turn is more likely
to partner with a 40-year-old gay male living in Munich than either of the
first two individuals.

Now there is actually an algorithm called Blossom V
<http://pub.ist.ac.at/~vnk/papers/BLOSSOM5.html> which given a set of such
agents will calculate optimally all the sexual partnerships, such that the
average distance for all the partnerships is minimised (It's called a
minimum cost perfect matching algorithm). It has two disqualifying
practical problems however. 1. It is very, very slow, far too slow for a
useful role in agent based models except for perhaps one that only needs to
be run occasionally on a small population on fast hardware. 2. It is
deterministic which is actually a poor feature for most stochastic
agent-based models. (It's also complicated.)

Stefan and I have developed matching algorithms that try to balance speed
and quality. We are currently exploring how this affects the outcomes of a
simulation. If we find the effect is substantial on say such bottom-line
outputs as overall prevalence, it might mean we have to increase our
scepticism/caution of simple models like Granich et al. However, if it
doesn't have a big effect then perhaps our confidence in their outputs
might be increased.

Here is preliminary work I did on this topic:
http://nathangeffen.webfactional.com/partnermatching/partnermatching.html

And this paper has interesting findings on the different outcomes modelling
various STIs  in South Africa using equation-based (Frequency-dependent)
models versus microsimulations (network models).
https://www.ncbi.nlm.nih.gov/pubmed/26859800

Stefan and I are working on at least two additional papers on this topic,
one of which is under peer-review.

Regards
Nathan Geffen
PhD student
University of Cape Town
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