Can societies be both safe and efficient? Different Scales of BioDefense:

Social interactions are key to transmission of infectious disease Oh dear. Germs

Societal structure and social organization shape social interactions Family Work Schools Social Gatherings Public Transportation Hospitals

Most of these are controlled at a societal level Family Work Schools Social Gatherings Public Transportation Hospitals

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

Some Bees Some Wasps Ants Termites So adorable and so useful!

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 4 Basic elements of concern:

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 M t 2. Rate of energy production for each task B t 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), S t 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 write I t,x In each iteration of the Markov process, each individual I t,x contributes to some P t,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 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 S t iterations  In each iteration, for each individual in P t,x there is a probability M t 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 P t,x and use M t 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 probabilities Prob(I t,x  I j  [T\t],x+1 )

1) Defined permanently by physiological caste When born, individuals are assigned at random into a permanent task So Prob(I t,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 So what were our strategies again?

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 B t =ρ 1 t, Decreasing linearly B t = ρ 1 ( |T|-t), Even B t =½ ρ 1 |T|  Increasing linearly S t = ρ 2 t, Decreasing linearly S t =ρ 2 |T|-t, Even S t =½ ρ 2 |T|  Increasing linearly M t =2 ρ 3 t, Decreasing linearly M t =ρ 3 2|T|-2t, Even M t = ρ 3 |T| ρ is some proportionality constant (in the examples shown, it’s just 1)

So what sorts of results do we see? These are averages from 1000 runs each random rep. castes age based

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? These graphs are from the Random strategy Random total s Random total bRandom total m

These graphs are from the Repertoire strategy Rep total s Rep total mRep total b

These graphs are from the age based strategy Age based total s Age based total bAge based total m

These graphs are from the castes strategy Castes total s Castes total bCastes total m

Random total pairs

Rep total pairs

Age-based total pairs

Castes total pairs 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

And from this we get: castes age rep. random

MPW work random rep age based castes

Random mpw s Random mpw b Random mpw m Random total s Random total b Random total m

Rep mpw s Rep mpw b Rep mpw m Rep total s Rep total m Rep total b

Age based mpw s Age based mpw b Age based mpw m Age based total s Age based total b Age based total m

Castes mpw s Castes mpw b Castes mpw m Castes total s Castes total b Castes total m

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

MPW work random rep age based castes Population Surviving Okay, these didn’t all fit so well random rep age based castes

Random mpw s Random mpw b Random mpw m Random total s Random total b Random total m

Rep mpw s Rep mpw b Rep mpw m Rep total s Rep total m Rep total b

Age based mpw s Age based mpw b Age based mpw m Age based total s Age based total b Age based total m

Castes mpw s Castes mpw b Castes mpw m Castes total s Castes total b Castes total m

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 D t to represent the density of infected individuals performing each task and make M t dependent on D t … 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!