Nina H. Fefferman, Ph.D. InForMID Tufts Univ. DIMACS Rutgers Univ. [email protected] Preparing Societal Infrastructure Against Disease-Related

Nina H. Fefferman, Ph.D.

InForMID Tufts Univ.DIMACS Rutgers Univ.

[email protected]

Preparing Societal Infrastructure Against Disease-Related Workforce Depletion

Disease can affect a large percentage of a population

This can be -

All at once

Over time

Such diseases pose not only direct threats, but indirect threats to the public health of a community

What do I mean?

Direct threats:Well

peopleSick people

Nothing terribly surprising about this

Pathogens of all sorts

Indirect threats:Well

people

Sick people

Some of the sick people have crucial jobs and they

can’t go to work

Well People who are

harmed by a lack of

provision of infrastructure

Basic idea behind this research :

Can we train or allocate our work force according to some algorithm in order to

minimize these sorts of problems?Due to time constraints, I’m going to show the ideas, not the

equations – if anyone wants the mathematical details, please just ask me after the talk!

What elements of the system do we want to incorporate?

Different tasks that need to be accomplished

Maybe each task has its own

1) rate of production

2) time to be trained

3) minimum number of workers needed

to accomplish anything

Let’s assume for today’s talk that risk of contracting disease, and the subsequent risk of death from

disease is uniform, regardless of task –

This may not be true if there is occupational exposure, or differential availability of medical

treatment based on employment

We will deal with all absence from work as “mortality” (permanent

absence from the workforce once absent once for any reason) –

Depending on the specific disease in question, this would definitely

want to be changed to reflect “duration of symptoms causing

absence from work” and “what is the probability of death from

infection”

Another strong and unlikely-to-be-correct assumption for today:

In addition to disease risk, we include an “additional risk of mortality” as a function

of how many tasks have fewer than the minimum number of workers needed to

accomplish themThis represents the indirect harm caused by the breakdown in infrastructure support – for the

models you’ll see here, it will be kept small (an order of magnitude less) relative to the direct

disease risk – this again would change once we had a specific problem/society to model

Given all of this, we can then simulate a population, with new workers being recruited into the

system, staying in or learning and progressing through new tasks over

time according to a variety of different strategies

We’ll start with four different allocation strategies

1. Defined permanently : only trained for one thing

2. Allocated by seniority : progress through different

tasks over time

3. Repertoire increases with seniority : build knowledge the

longer you work

4. Completely random : just for comparison, everyone switches at random

(Suggested by the most efficient working

organizations of the natural world – social

insects!)

(Determined)

(Discrete)

(Repertoire)

(Random)

So within the model, we are concerned with :

1. Direct disease/mortality risk (constant in all

tasks t), DRiskt

2. Indirect mortality risk, IRiskt

3. Rate of production for each task, Bt

4. Cost of switching to task t from some other task, St

5. Minimum number of individuals in task t in order to be successful, Mt

For today, we’ll run this with t=20, Bt=t, St=t, and t DRiskt=0.01, IRiskt=0.001*(# tasks

that have failed)

And we’ll look at two scenarios of Mt :

1) Mt=21-t and 2) t Mt=5

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 (and I do in the paper) – 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 step 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

2) The individual doesn’t contribute during the ‘learning phase’

In each iteration, for each living individual in Pt,x

there is an associated probability (IRiskt + DRiskt) of dying (independent for each individual)

Individuals also die (deterministically) if they exceed a (iteration based) maximum life span (500 time steps – arbitrarily chosen)

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 : Add 10 new individuals every time

step (arbitrary)

Then for each iteration (x), the total amount of work produced is for each t

We also keep track of how much of the population is “left alive”, since there is a potential conflict between

“work production” and population survival

xttPB ,

So, given all this, what are our results?

Constant Exposure

Seasonal Exposure

Deterministic Strategy – Different scenariosDeterministic – Const. Exposure

– ↓ Minimum #s

Deterministic – Const. Exposure

– Const. Minimum #s

Deterministic – Seas. Exposure

– ↓ Minimum #s

Deterministic – Seas. Exposure


Constant Exposure

Seasonal Exposure

Discrete Strategy – Different scenarios

Discrete – Const. Exposure

– ↓ Minimum #s



Discrete – Seas. Exposure – ↓ Minimum #s

Discrete – Seas. Exposure – Const. Minimum #s

Constant Exposure

Seasonal Exposure

Repertoire Strategy – Different scenarios

Repertoire Repertoire

RepertoireRepertoire – Const.

Exposure – ↓ Minimum #s

Repertoire – Const. Exposure


Repertoire – Seas. Exposure

– ↓ Minimum #s



Constant Exposure

Seasonal Exposure

Random Strategy – Different scenarios

Random – Const. Exposure

– ↓ Minimum #s



Random – Seas. Exposure – ↓ Minimum #s

Random – Seas. Exposure – Const. Minimum #s

So what if we compare within the same scenario, across strategies:Let’s compare across strategies for Constant Exposure, Constant M

Repertoire









What about for Seasonal Exposure, Constant M Deterministic – Seas.

Exposure – Const. Minimum #s

Discrete – Seas. Exposure – Const. Minimum #s



Random – Seas. Exposure – Const. Minimum #s

And for Constant Exposure, Decreasing MDeterministic – Const.

Exposure – ↓ Minimum #s


– ↓ Minimum #s


– ↓ Minimum #s


– ↓ Minimum #s

And for Seasonal Exposure, Decreasing MDeterministic – ↓ Exposure

– ↓ Minimum #sDiscrete – ↓ Exposure

– ↓ Minimum #s

Repertoire – ↓ Exposure – ↓ Minimum #s

Random – ↓ Exposure – ↓ Minimum #s

Those are the results from the work produced

What about the number left living?

But just to check, did the indirect mortality actually make a difference?

Not really – if the

strategy is Determinis

tic

These figures are all taken only from the scenarios of

constant disease and even minimum numbers required



Without Infrastructure Compounded Mortality

It makes a huge

difference if the

strategy is Discrete




It makes a huge

difference if the

strategy is Repertoire




Not Really – if the

strategy is Random




Take home messages:These studies are by no means the “answer” to anything, but they are a good way to start examining these sorts of questions

The more specific a disease and population and infrastructure we want to examine, the more appropriately we can tailor the simulations

It’s unlikely that these sorts of models will provide “easy” answers – but it IS likely that they could provide public policy makers with “likely disease-related repercussions” of societal organization policies

Any Questions?!

My thanks to The organizers for inviting me

The NSF for funding to DIMACS, where I have been happily visiting for the past year

InForMID for additional support

All of you for your time and interest

Please feel free to contact me with further

questions later!

Documents

Nina H. Fefferman, Ph.D. InForMID Tufts Univ. DIMACS Rutgers Univ. [email protected] Preparing Societal Infrastructure Against Disease-Related