Different Scales of BioDefense:
Can societies be
both safe and
efficient?
Social interactions are key to transmission of
infectious disease
Oh dear.
Germs
Societal structure and social organization
shape social interactions
Work
Family
Schools
Hospitals
Social
Gatherings
Public
Transportation
Most of these are controlled at a societal level
Work
Family
Schools
Hospitals
Social
Gatherings
Public
Transportation
But even saying “societal” may be too broad
We’ve actually got a variety of scales:
• individual
• neighborhood
• company
• local
• national
• international
Each scale probably leads to a different
robustness goal
So, could there be ways to structure societies
to maximize robustness to disease?
What could the ‘maximal robustness’ goals be?
1. Minimizing the number of infections
2. Minimizing the number of deaths
Or maybe we’re more concerned about societal effects
3. Minimizing the economic costs
4. Minimizing the effect on population growth
5. Minimizing crowding in hospitals
6. Minimizing the compromise of societal infrastructure
(keeping a minimum number of people in crucial positions at all times)
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 doesn’t interfere with a functioning society
Ideas welcome
Each of these goals leads us to a different
question & (for now) a different model
Today we’ll 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, we’ve 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
Starting on the largest scale:
We got to this point by thinking about social
interactions guiding exposure risks, but let’s 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 it’s planning stage
To answer questions about economic and
infrastructure efficiency, we need a way to
represent costs and benefits and disease risk
To start with, let’s look at the simplest trade-off
system
Yes folks, that’s right…
It’s 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
So adorable
and so useful!
Termites
Some Bees
Ants
Some Wasps
4 Basic elements of concern:
Amount of
‘work’ in
each task
completed in
each unit of
time
Age of
worker
Disease risk
associated
with task
completion
Is the task
currently a
limiting
factor for the
colony?
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?
Examples of what I mean:
1. 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
2. Termites are (comparatively) quite bad at combating
pathogen risks –
 So we would expect that they should sacrifice colony performance in favor
of greater safety
3. Honey bees are differentially susceptible to pathogens
based on age –
 So we might expect an age-specific exploitation of labor
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 doesn’t hurt to keep in mind that it might
not be true
Model formulation –
(discrete)
Three basic counterbalancing parameters:
1. Mortality risks for each task Mt
2. Rate of energy production for each task Bt
3. 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 statedependent Markov process of successive checks of
randomly generated values against threshold values
Notice that we actually can write this in closed
form – we don’t 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
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 doesn’t contribute if they are dead
 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, that’s 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)
2) The individual doesn’t contribute if they are in the ‘learning phase’
 They’re in the learning phase if they’ve switched into their current task
(t) for less than
St iterations
We also replenish the population periodically: every 30
iterations, we add 30 new individuals
This mimics the oviposition patterns of termites, we’d change
it for other social insect species
Then for each iteration (x), the total amount of
work produced is  Bt Pt , x
t
And the total for all the iterations is just
 B P
t t,x
x
t
Now we just need to define the different task
allocation strategies as transition probabilities
Prob(It,x  Ij[T\t],x+1)
So what were our strategies again?
1) 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 t=a
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
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=ρ1t, Decreasing linearly Bt= ρ1(|T|-t),
Even Bt=½ ρ1|T|
 Increasing linearly St= ρ2t, Decreasing linearly St=ρ2|T|-t,
Even St=½ ρ2|T|
 Increasing linearly Mt=2 ρ3t, Decreasing linearly Mt=ρ32|T|-2t,
Even Mt= ρ3|T|
ρ is some proportionality constant (in the examples shown, it’s just 1)
3,000,000
2,500,000
bd, md, sd
bd, md, se
bd, md, si
bd, me, sd
bd, me se
bd, me, si
bd, mi, sd
bd, mi, se
bd, mi, si
be, md, sd
be, md, se
be, md, si
be, me, sd
be, me, se
be, me, si
be, mi, sd
be, mi, se
be, mi, si
bi, md, sd
bi, md, se
bi, md, si
bi, me, sd
bi, me, se
bi, me, si
bi, mi, sd
bi, mi, se
bi, mi, si
So what sorts of results do we see?
Total work
3,500,000
random
random
rep.
rep
age based
discrete
castes
determined
2,000,000
1,500,000
1,000,000
500,000
0
These are averages from 1000 runs each
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 don’t know
anything about the risks or benefits or switching costs of each tasks?
Total work
1,400,000
1,200,000
1,000,000
800,000
stdev
average
600,000
400,000
200,000
0
Random
random
Rep
rep
Discrete
age
based
Determined
castes
What if we only know one thing?
Random total b
Random total
Random
total m
Random Total
800,000
800,000
700,000
700,000
600,000
600,000
500,000
500,000
stdev
average
400,000
stdev
average
400,000
300,000
300,000
200,000
200,000
100,000
100,000
0
0
bd
be
md
bi
me
Random total s
Random total
800,000
700,000
600,000
These graphs
are from the
Random
strategy
500,000
stdev
average
400,000
300,000
200,000
100,000
0
sd
se
si
mi
Rep total b
Rep
total b
Rep total m
Rep
total m
2,000,000
2,000,000
1,800,000
1,800,000
1,600,000
1,600,000
1,400,000
1,400,000
1,200,000
1,200,000
stdev
average
1,000,000
stdev
average
1,000,000
800,000
800,000
600,000
600,000
400,000
400,000
200,000
200,000
0
0
bd
be
md
bi
me
Rep total S
Rep
total s
2,000,000
1,800,000
These graphs
are from the
Repertoire
strategy
1,600,000
1,400,000
1,200,000
stdev
average
1,000,000
800,000
600,000
400,000
200,000
0
sd
se
si
mi
b
AgeDiscrete
basedtotal
total
b
m
AgeDiscrete
basedtotal
total
m
2,500,000
2,500,000
2,000,000
2,000,000
1,500,000
1,500,000
stdev
average
stdev
average
1,000,000
1,000,000
500,000
500,000
0
0
bd
be
bi
md
me
s s
AgeDiscrete
basedtotal
total
2,500,000
These graphs
are from the
age based
strategy
2,000,000
1,500,000
stdev
average
1,000,000
500,000
0
sd
se
si
mi
Castes total b
Determined total m
Castes
total m
Determined total b
800,000
800,000
700,000
700,000
600,000
600,000
500,000
500,000
300,000
300,000
200,000
200,000
100,000
100,000
0
0
bd
be
stdev
average
400,000
stdev
average
400,000
md
bi
me
Castes total s
Determined total s
800,000
These graphs
are from the
castes
strategy
700,000
600,000
500,000
stdev
average
400,000
300,000
200,000
100,000
0
sd
se
si
mi
bd md
bd me
bd mi
bd sd
bd se
bd si
md be
md bi
md sd
md se
md si
sd be
sd bi
sd me
sd mi
be me
be mi
be se
be si
me bi
me se
me si
se bi
se mi
bi mi
bi si
mi si
Random
Randomtotal
totalpairs
pairs
1,200,000
1,000,000
800,000
600,000
stdev
average
400,000
200,000
0
bd md
bd me
bd mi
bd sd
bd se
bd si
md be
md bi
md sd
md se
md si
sd be
sd bi
sd me
sd mi
be me
be mi
be se
be si
me bi
me se
me si
se bi
se mi
bi mi
bi si
mi si
Reptotal
totalpairs
Rep
3,500,000
3,000,000
2,500,000
2,000,000
stdev
average
1,500,000
1,000,000
500,000
0
bd md
bd me
bd mi
bd sd
bd se
bd si
md be
md bi
md sd
md se
md si
sd be
sd bi
sd me
sd mi
be me
be mi
be se
be si
me bi
me se
me si
se bi
se mi
bi mi
bi si
mi si
Age-based
total
pairs
Discrete total
pairs
3,500,000
3,000,000
2,500,000
2,000,000
stdev
average
1,500,000
1,000,000
500,000
0
Determined
totalpairs
pairs
Castes total
800,000
700,000
600,000
500,000
stdev
average
400,000
300,000
200,000
100,000
bd md
bd me
bd mi
bd sd
bd se
bd si
md be
md bi
md sd
md se
md si
sd be
sd bi
sd me
sd mi
be me
be mi
be se
be si
me bi
me se
me si
se bi
se mi
bi mi
bi si
mi si
0
But, alas, this is not the whole picture
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
For every given chunk of time, we choose one of the
tasks to be “the most pressing” task of the moment (i)
We don’t 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 Bi Pi , x
And for all iterations is
B P
i i,x
x
The most pressing task changes every 100 iterations and is selected
at random from T
5.400
bd, md, sd
bd, md, se
bd, md, si
bd, me, sd
bd, me se
bd, me, si
bd, mi, sd
bd, mi, se
bd, mi, si
be, md, sd
be, md, se
be, md, si
be, me, sd
be, me, se
be, me, si
be, mi, sd
be, mi, se
be, mi, si
bi, md, sd
bi, md, se
bi, md, si
bi, me, sd
bi, me, se
bi, me, si
bi, mi, sd
bi, mi, se
bi, mi, si
And from this we get:
Called for work
5.600
random
random
rep
rep.
age
discrete
castes
determined
5.200
5.000
4.800
4.600
4.400
MPW work
Called for
5.3 0 0 0 0
5.2 50 0 0
5.2 0 0 0 0
5.1
50 0 0
5.1
0000
st dev
5.0 50 0 0
aver age
5.0 0 0 0 0
4 .9 50 0 0
4 .9 0 0 0 0
4 .8 50 0 0
4 .8 0 0 0 0
Rand o m
random
Rep
rep
Discr et e
age based
Det er mined
castes
Total work
1,400,000
1,200,000
1,000,000
800,000
stdev
average
600,000
400,000
200,000
0
Random
random
Discrete castes
Determined
repRep age based
Random cfw b
Random
mpw b
Random Total
Random total b
800,000
5.10
700,000
5.05
600,000
500,000
5.00
stdev
average
4.95
stdev
average
400,000
300,000
200,000
4.90
100,000
4.85
0
bd
be
bi
bd
Random cfw m
Random mpw m
5.10
be
bi
Random total m
Random total
800,000
700,000
5.05
600,000
5.00
500,000
stdev
average
4.95
stdev
average
400,000
300,000
4.90
200,000
100,000
4.85
md
me
0
mi
md
Random cfw s
Random
mpw s
me
mi
Random total
Random total s
5.10
800,000
5.05
700,000
600,000
5.00
stdev
average
500,000
stdev
average
400,000
4.95
300,000
4.90
200,000
100,000
4.85
sd
se
si
0
sd
se
si
Rep total b
Rep total b
Rep cfw b
Rep mpw b
2,000,000
5.35
1,800,000
5.30
1,600,000
5.25
1,400,000
5.20
1,200,000
5.15
stdev
average
5.10
stdev
average
1,000,000
800,000
5.05
5.00
600,000
4.95
400,000
4.90
200,000
0
4.85
bd
be
bd
bi
be
bi
Rep total m
Rep total m
Rep cfw m
Rep mpw m
2,000,000
5.35
1,800,000
5.30
1,600,000
5.25
1,400,000
5.20
1,200,000
5.15
stdev
average
5.10
5.05
stdev
average
1,000,000
800,000
600,000
5.00
400,000
4.95
200,000
4.90
0
4.85
md
me
md
mi
me
mi
Rep total s
Rep total S
Rep cfw s
Rep mpw s
2,000,000
5.35
1,800,000
5.30
1,600,000
5.25
1,400,000
5.20
1,200,000
5.15
stdev
average
5.10
stdev
average
1,000,000
800,000
5.05
600,000
5.00
400,000
4.95
200,000
4.90
0
4.85
sd
sd
se
si
se
si
Discrete cfw b
Age based
mpw b
Discrete total b
5.40
Age based total b
2,500,000
5.30
2,000,000
5.20
1,500,000
stdev
average
5.10
stdev
average
1,000,000
5.00
4.90
500,000
4.80
bd
be
0
bi
bd
cfw mpw
m
AgeDiscrete
based
m
be
bi
Discrete total m
5.40
Age based total m
2,500,000
5.30
2,000,000
5.20
1,500,000
stdev
average
stdev
average
5.10
1,000,000
5.00
500,000
4.90
0
md
4.80
md
me
me
mi
mi
s
AgeDiscrete
basedtotal
total
s
Age based mpw s
Discrete cfw s
2,500,000
5.40
2,000,000
5.30
5.20
1,500,000
stdev
average
stdev
average
5.10
1,000,000
5.00
500,000
4.90
0
4.80
sd
se
si
sd
se
si
Determined
cfw b b
Castes
mpw
Determined total b
Castes total b
5.15
800,000
5.10
700,000
5.05
600,000
500,000
5.00
stdev
average
stdev
average
400,000
4.95
300,000
4.90
200,000
4.85
100,000
4.80
0
bd
be
bi
bd
Determined cfw m
Castes
mpw m
be
bi
Determined total m
5.15
800,000
5.10
700,000
Castes total m
600,000
5.05
500,000
5.00
stdev
average
4.95
stdev
average
400,000
300,000
4.90
200,000
4.85
100,000
0
4.80
md
me
md
mi
Determined cfw s
Castes mpw s
me
mi
Castes total s
Determined total s
5.15
800,000
5.10
700,000
5.05
600,000
500,000
5.00
stdev
average
4.95
stdev
average
400,000
300,000
4.90
200,000
4.85
100,000
4.80
sd
se
si
0
sd
se
si
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
Population
Surviving
Population
at End
350
300
250
200
stdev
average
150
100
50
0
Random
Rep build
Discrete
Determined
MPW work
Called for
5.3 0 0 0 0
5.2 50 0 0
5.2 0 0 0 0
5.1
50 0 0
5.1
0000
Okay, these
didn’t all fit
so well
st dev
5.0 50 0 0
aver age
5.0 0 0 0 0
4 .9 50 0 0
4 .9 0 0 0 0
4 .8 50 0 0
4 .8 0 0 0 0
Rand o m
Rep
random
Discr et e
rep
age based
Det er mined
castes
Total work
Population
Surviving
Population at End
350
300
1,400,000
1,200,000
1,000,000
250
800,000
200
stdev
stdev
average
average
150
600,000
100
400,000
50
200,000
0
Random
random
Rep build
rep
Discrete
age based
Determined
castes
0
Random
random
Discrete castes
Determined
repRep age based
Random
mpw b
5.05
Random Pop b
Random Total
Random cfw b
5.10
Random
total b
800,000
700,000
600,000
140
120
500,000
100
5.00
stdev
average
stdev
average
400,000
80
300,000
4.95
stdev
average
60
200,000
4.90
100,000
40
0
4.85
bd
be
bd
bi
be
bi
20
0
bd
be
bi
Random pop m
Random cfw m
Random
mpw m
5.10
5.05
Random total
700,000
600,000
5.00
140
Random
total m
800,000
120
100
500,000
stdev
average
4.95
80
average
60
300,000
200,000
4.90
stdev
stdev
average
400,000
40
100,000
20
4.85
md
me
0
mi
md
me
mi
0
md
Random
mpw s
me
mi
Random cfw s
5.10
5.05
Random pop s
Random total
Random
total s
800,000
700,000
600,000
5.00
140
120
500,000
stdev
average
stdev
average
400,000
100
4.95
300,000
80
stdev
200,000
4.90
average
60
100,000
4.85
0
sd
se
si
sd
se
si
40
20
0
sd
se
si
Rep mpw b
Rep pop b
Rep total b
Rep total b
Rep cfw b
5.35
2,000,000
5.30
1,800,000
400
5.25
1,600,000
350
5.20
1,400,000
5.15
300
1,200,000
stdev
average
5.10
5.05
800,000
5.00
600,000
4.95
400,000
4.90
200,000
4.85
0
bd
be
stdev
average
1,000,000
bi
250
stdev
200
average
150
100
50
bd
be
bi
0
bd
be
bi
Rep pop m
Rep mpw m
Rep cfw m
5.35
Rep total m
Rep total m
2,000,000
400
5.30
1,800,000
350
5.25
1,600,000
300
5.20
1,400,000
5.15
250
1,200,000
stdev
average
5.10
5.05
800,000
5.00
600,000
4.95
400,000
4.90
200,000
4.85
0
md
me
stdev
average
1,000,000
average
150
100
50
md
mi
stdev
200
me
0
mi
md
me
mi
Rep pop s
Rep mpw s
Rep total S
Rep total s
Rep cfw s
5.35
2,000,000
5.30
1,800,000
5.25
1,600,000
5.20
1,400,000
5.15
1,200,000
stdev
average
5.10
400
350
300
250
stdev
average
1,000,000
5.05
800,000
5.00
600,000
4.95
400,000
4.90
200,000
sd
se
si
average
150
100
50
0
4.85
stdev
200
sd
se
si
0
sd
se
si
Age based
mpw b
Discrete cfw b
5.40
5.30
Discrete total b
Age based
total b
2,500,000
2,000,000
Age based pop b
100
90
80
5.20
1,500,000
70
stdev
average
5.10
stdev
average
60
1,000,000
5.00
stdev
50
average
40
30
500,000
4.90
20
4.80
bd
be
10
0
bi
bd
be
bi
0
bd
Discrete cfw m
Age
based
mpw m
5.40
5.30
2,000,000
bi
Age based pop m
Discrete total m
Age based
total m
2,500,000
be
100
90
80
5.20
70
60
1,500,000
stdev
average
5.10
stdev
average
average
40
1,000,000
5.00
stdev
50
30
4.90
500,000
4.80
0
20
10
0
md
me
mi
md
5.30
md
mi
Age based
total s
me
mi
Discrete total s
Discrete cfw s
Age based mpw
s
5.40
me
2,500,000
Age based pop s
100
2,000,000
90
80
5.20
70
1,500,000
stdev
average
5.10
stdev
average
1,000,000
5.00
60
stdev
50
average
40
30
4.90
500,000
20
10
4.80
sd
se
si
0
0
sd
se
si
sd
se
si
Determined cfw b
Castes
mpw b
Determined total b
5.15
800,000
5.10
700,000
Castes total b
Castes pop b
16
14
600,000
5.05
12
500,000
10
5.00
stdev
average
4.95
stdev
average
400,000
300,000
200,000
4
4.85
100,000
2
4.80
0
be
be
bi
bd
800,000
16
700,000
5.10
14
600,000
5.05
12
500,000
5.00
stdev
average
4.95
stdev
average
400,000
200,000
4.85
100,000
4.80
0
me
10
stdev
8
300,000
4.90
average
6
4
2
md
mi
me
mi
0
md
Determined cfw s
Determined total s
Castes mpw s
5.15
Castes total s
800,000
me
mi
Castes pop s
16
700,000
5.10
bi
Castes pop m
Castes total m
Determined cfw m
md
be
Determined total m
Castes mpw m
5.15
0
bd
bi
average
6
4.90
bd
stdev
8
14
600,000
5.05
12
500,000
10
5.00
stdev
average
stdev
average
400,000
stdev
8
average
4.95
4.90
4.85
300,000
6
200,000
4
2
100,000
4.80
0
0
sd
se
si
sd
se
si
sd
se
si
This research is ongoing, so I
haven’t 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
As a next step, to more
accurately reflect social
interaction governing disease
dynamics, even at this scale, it’s
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 that’s the plan
This work is ongoing and is in collaboration
with Sam Beshers at University of Illinois
at Urbana-Champaign
I’m also now working
on shifting the
parameter structure a
little to reflect human
societies with Ramanan
Laxminarayan (thanks
to DIMACS!)
Thanks very much!