Can societies be both safe and efficient?

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Different Scales of BioDefense
Can societies be both safe and efficient?
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Social interactions are key to transmission of
infectious disease
Oh dear.
Germs
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Societal structure and social organization shape
social interactions
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Most of these are controlled at a societal level
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But even saying societal may be too broad

• Weve actually got a variety of scales
• individual
• neighborhood
• company
• local
• national
• international
• Each scale probably leads to a different
  robustness goal

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So, could there be ways to structure societies to
maximize robustness to disease?

• What could the maximal robustness goals be?
• Minimizing the number of infections
• Minimizing the number of deaths
• Or maybe were more concerned about societal
  effects
• Minimizing the economic costs
• Minimizing the effect on population growth
• Minimizing crowding in hospitals
• Minimizing the compromise of societal
  infrastructure
• (keeping a minimum number of people in crucial
  positions at all times)

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Pipe Dream 1 To build a single model of
infectious disease epidemiology that
incorporates measures of each of these effects
and, weighting each goal according to our
policies/needs, tells us how to re-structure
social interactions in a minimally intrusive way
that still doesnt interfere with a functioning
society
Ideas welcome
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Each of these goals leads us to a different
question (for now) a different model
Today well focus on a model that can be
interpreted to examine both 3. Minimizing the
economic costs 6. Minimizing the
compromise of societal infrastructure In
previous talks, weve discussed a few experiments
that focused on 4. Minimizing the effect on
population growth 5. Minimizing crowding in
hospitals If you would like to refresh your
memory on those, please talk to me later
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Starting on the largest scale We got to this
point by thinking about social interactions
guiding exposure risks, but lets pull back for a
bit and think only about primary exposure This
should let us focus on the efficiency question
and then we can add back the layers of complexity
for individual secondary exposure
We talked briefly about this work when it was in
its planning stage
To answer questions about economic and
infrastructure efficiency, we need a way to
represent costs and benefits and disease risk
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To start with, lets look at the simplest
trade-off system
Yes folks, thats right Its another termite
talk!

• Once again, social insects provide all of the
  crucial facets of social organization without
  most of the incredible complexities of humans
• They need to complete a variety of tasks, as a
  society
• Each task has different associated primary
  exposure risks

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So adorable and so useful!
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4 Basic elements of concern
Age of worker
Amount of work in each task completed in each
unit of time
Is the task currently a limiting factor for the
colony?
Disease risk associated with task completion
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How do they all relate?
In social insects, there are four basic theories
for task allocation decisions 1) Defined
permanently by physiological caste 2) Determined
by age 3) Repertoire increases with age 4)
Completely random So which does better under what
assumptions of pathogen risk? And can we predict
a social organization by what we know about the
different pathogen risks of different insects?
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Examples of what I mean

• We know that some ants are really good at
  combating pathogens by glandular secretions
• Their social organization should be willing to
  compromise safety for greater efficiency since
  they can handle the risks individually
• Termites are (comparatively) quite bad at
  combating pathogen risks
• So we would expect that they should sacrifice
  colony performance in favor of greater safety
• Honey bees are differentially susceptible to
  pathogens based on age
• So we might expect an age-specific exploitation
  of labor

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So what do we do
First we make a basic assumption that disease
risk is a substantial and independent selective
pressure, operating on a population-wide level,
during the evolutionary history of social
insects This is probably not a bad assumption,
but it doesnt hurt to keep in mind that it might
not be true
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Model formulation (discrete)

• Three basic counterbalancing parameters
• Mortality risks for each task Mt
• Rate of energy production for each task Bt
• The cost of switching to task t from some other
  task (either to learn how, or else to get to
  where the action is), St

We simulate the following via a stochastic
state-dependent Markov process of successive
checks of randomly generated values against
threshold values
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Notice that we actually can write this in closed
form we dont need to simulate anything
stochastically to get meaningful results HOWEVER
part of what we want to see is the range and
distribution of the outcome when we incorporate
stochasticity into the process
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• We have individuals I and tasks (t) in iteration
  (x), so we write It,x
• In each iteration of the Markov process, each
  individual It,x contributes to some Pt,x the size
  of the population working on their task (t) in
  iteration (x) EXCEPT
• 1) The individual doesnt contribute if
  they are dead
• 2) The individual doesnt contribute if they
  are in the learning phase
• Theyre in the learning phase if theyve
  switched into their current task (t) for less
  than St iterations

• In each iteration, for each individual in Pt,x
  there is a probability Mt of dying from task
  related pathogen exposure and once you die,
  thats it, you stay dead
• To run the model, for every x, we generate an
  independent random value 0,1 for each
  individual in Pt,x and use Mt as a threshold
  above survives, below dies
• Individuals also die if they exceed a maximum
  life span (iteration based)

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We also replenish the population periodically
every 30 iterations, we add 30 new
individuals This mimics the oviposition patterns
of termites, wed change it for other social
insect species
Then for each iteration (x), the total amount of
work produced is
And the total for all the iterations is just
Now we just need to define the different task
allocation strategies as transition probabilities
Prob(It,x ? Ij?T\t,x1)
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So what were our strategies again?

• Defined permanently by physiological caste
• When born, individuals are assigned at random
  into a permanent task
• So Prob(It,1)1/T for each t and is then
  constant over all x
• 2) Determined by age
• We assign individuals into T age classes and
  for age class a, we deterministically assign the
  individual into task ta
• 3) Repertoire increases with age
• Individuals in each age class a choose at random
  from among the first a tasks
• 4) Completely random
• Individuals change tasks when they change age
  classes, but switch into any other task
• Transition from one age class into another is
  defined to happen every (life span/T) iterations

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Now we can examine how these strategies do in the
face of different relationships among the
parameters

• Suppose that we choose some combination of the
  following
• Increasing linearly Bt?1t, Decreasing linearly
  Bt ?1(T-t),
• Even Bt½ ?1T
• Increasing linearly St ?2t, Decreasing linearly
  St?2T-t,
• Even St½ ?2T
• Increasing linearly Mt2 ?3t, Decreasing
  linearly Mt?32T-2t,
• Even Mt ?3T
• ? is some proportionality constant (in the
  examples shown, its just 1)

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So what sorts of results do we see?
These are averages from 1000 runs each
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But what can this help us to say about social
structure and pathogen exposure risks? This
becomes a matter of prior knowledge What
relationships between the parameters do we know
we can expect? How can we structure society
based on that knowledge?
This last graph was complete knowledge, but
what if we dont know anything about the risks or
benefits or switching costs of each tasks?
random rep age based castes
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What if we only know one thing?
Random total b
Random total m

Random total s
These graphs are from the Random strategy
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Rep total m
Rep total b
Rep total s
These graphs are from the Repertoire strategy
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Age based total b
Age based total m
Age based total s
These graphs are from the age based strategy
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Castes total b
Castes total m
Castes total s
These graphs are from the castes strategy
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Random total pairs
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Rep total pairs
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Age-based total pairs
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Castes total pairs
But, alas, this is not the whole picture
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Sometimes we need specific tasks more than usual,
or more than any other how do we hedge our bets
to make sure that we can always have enough
workers to devote to those when we need
them? This could be thought of as a buffer zone
for each task against that task becoming rate
limiting
Maintaining this buffer zone might be at odds
with maximizing efficiency, even under the same
pathogen exposure risks
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For every given chunk of time, we choose one of
the tasks to be the most pressing task of the
moment (i) We dont ask any individuals to switch
which task they perform, we just measure only how
much work is produced in the most pressing task
So instead, for each iteration (x), the total
amount of most pressing work produced is
And for all iterations is
The most pressing task changes every 100
iterations and is selected at random from T
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And from this we get
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So we have a few cases where making the colony
the most efficient, even under the same parameter
scenarios should lead us to a different choice
than if we were trying to make sure that our
buffer against being unable to complete the most
important tasks of the moment is sufficiently
large And we compare each of these with the
mortality costs by looking at the size of the
population left alive
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MPW work
Okay, these didnt all fit so well
random rep age based castes
random rep age based
castes
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This research is ongoing, so I havent finished
all the interpreting of results yet, however,
clearly we have a few points of trade-off A
society as a whole needs to balance survival
against efficiency against buffering in
incredibly complex ways, but this allows a first
step into examining those trade-offs
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As a next step, to more accurately reflect social
interaction governing disease dynamics, even at
this scale, its time to introduce a new variable
Dt to represent the density of infected
individuals performing each task and make Mt
dependent on Dt At least thats the plan
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This work is ongoing and is in collaboration
with Sam Beshers at University of Illinois at
Urbana-Champaign
Im also now working on shifting the parameter
structure a little to reflect human societies
with Ramanan Laxminarayan (thanks to
DIMACS!) Thanks very much!