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Different Scales of BioDefense:

Can societies be both safe and efficient?

Societal structure and social organization shape social interactions

Schools

Family

Hospitals

Work

Social Gatherings

Public Transportation

Family

Hospitals

Work

Social Gatherings

PublicTransportation

Most of these are controlled at a societal level

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?
- Minimizing the number of infections
- Minimizing the number of deaths
- Or maybe we’re 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)

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

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

- 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?

- 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

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:
- 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

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 writeIt,x

- In each iteration of the Markov process, each individual It,x contributes to some Pt,xthe size of the population working on their task (t) in iteration (x) EXCEPT
- 1) The individual doesn’t contribute if they are dead
- 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

- 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)

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

And the total for all the iterations is just

Now we just need to define the different task allocation strategies as transition probabilitiesProb(It,xIj[T\t],x+1)

So what were our strategies again?

- Defined permanently by physiological caste
- When born, individuals are assigned at random into a permanent task
- SoProb(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)

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?

random rep age based castes

What if we only know one thing?

Random total b

Random total m

Random total s

These graphs are from the Random strategy

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

And for all iterations is

The most pressing task changes every 100 iterations and is selected at random from T

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

random rep age based castes

MPW work

Okay, these didn’t all fit so well

random rep age based castes

random rep age based castes

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!

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