Agent Simulation Using Path Telemetry for Modeling COVID-19

Workplace Hazard and Risk

David Beymer

, Vandana Mukherjee

, Anup Pillai

, Hakan Bulu

, Vanessa Burrowes

James Kaufman

1,∗

and Ed Seabolt

IBM Research - Almaden, 650 Harry Rd, San Jose, CA 95120, U.S.A.

IBM, 3039 E Cornwallis Rd, Research Triangle Park, NC 27709, U.S.A.

Keywords:

Computer Simulation, Agent-Based Modeling, Epidemiological Modeling, Risk Analysis, Safety

Management.

Abstract:

We present a cloud native agent based simulation of disease transmission hazard and risk in a model of a

particular workplace. When combined with epidemiological data for employee home counties, the simulation

can be used to measure the effect of interventions and building policies on occupational hazard and risk from

an infectious disease, and to compare that hazard and risk to the average risk to the employees in their home

counties based on current outbreak data. We demonstrate this for two particular interventions, varying the

number of employees allowed to work onsite, and enabling/disabling alternate routes at choke points such

as cafeteria checkpoints. We discuss how occupational hazard and risk depends strongly on the details of

workplace layout and policies and propose how the current simulation (and tools like it) can be used to evaluate

policies and procedures for return to work.

1 INTRODUCTION

The pandemic disease COVID-19, caused by

the SARS-CoV-2 virus, disrupted economies and

lifestyles worldwide. As new variants continued to

evolve and emerge, many organizations struggled to

develop consistent and robust guidelines for policies

that supported a ”safe” return to work. The process is

confounded as the rates of viral transmission change

with the evolution of the virus as it adapts to human

host populations as well as to the changing landscape

of host immunity.

Understanding which policies might best support

a ”safe” return to work ﬁrst requires an agreed deﬁ-

nition of safety, along with quantitative measures for

both hazard and risk (Hosseini et al., 2017; Kumpu-

lainen, 2006; Sage and White, 1980). Assessment of

occupational risk requires quantiﬁcation of the poten-

tial hazards a person encounters in a workplace envi-

ronment (Daniels et al., 2020). No workplace is com-

pletely free of risk, but in the context of infectious

disease exposure one might classify a workplace as

∗

J. Kaufman is currently with Altos Labs, Bay Area

Institute of Science, 1300 Island Drive, Redwood City, CA

94065, U.S.A.

”safe” if the exposure hazard and disease transmission

risk are less than the corresponding hazards and risks

an individual might face in the same time span had

they not come to the workplace. This baseline risk de-

pends, of course, on interventions, policies, and prac-

tices in their jurisdiction of residence, but the data re-

quired to measure local hazard and risk is currently

available in most jurisdictions through local public

health reporting. In this paper we apply epidemio-

logical compartment modeling (Gopalakrishnan et al.,

2021b; Gopalakrishnan et al., 2021a; Baldassi et al.,

2021; Douglas et al., 2019; Bianco et al., 2021) to the

home counties of employees in a simulated workforce

to drive an agent based simulation of a real workplace.

Agent-based models, which have been used in a

variety of ﬁelds such as economics, business, gaming

and the social sciences, construct a simulated environ-

ment of independent agents, from whose simple rules

of interaction an emergent system behavior arises.

Agent based modeling has been used to study how

workplace policies and practices inﬂuence workplace

outcomes across a variety of dimensions (Mu

noz and

Iglesias, 2021; Duggirala et al., 2016; Hardy et al.,

2021; Vitins et al., 2016). Some agent-based sys-

tems have included strong spatial support, such as the

use of GIS concepts in the GAMA platform (Tail-

Beymer, D., Mukherjee, V., Pillai, A., Bulu, H., Burrowes, V., Kaufman, J. and Seabolt, E.

Agent Simulation Using Path Telemetry for Modeling COVID-19 Workplace Hazard and Risk.

DOI: 10.5220/0012322400003657

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2024) - Volume 1, pages 417-428

ISBN: 978-989-758-688-0; ISSN: 2184-4305

417

landier et al., 2018), and social simulations built on

top (BEN system (Bourgais et al., 2019)). When

applied to epidemiology, the agent-based model al-

lows for social networks between the agents to be

studied for their impact on viral dynamics. In (Kerr

et al., 2021; Hinch et al., 2021; Chang et al., 2020),

agent networks are formed consisting of households,

schools, workplaces, and random connections for in-

teractions with the community-at-large. An epidemi-

ological model is placed over the agents, and the ef-

fects of different simulated COVID-19 interventions

such as masks, contact tracing, or quarantine can be

studied. With the agent network, one could model,

for instance, how a virus can be transmitted from a

school to a workplace via child-to-parent infection in

a household. The OpenCOVID (Shattock et al., 2022)

agent simulation system constructs an agent network

based on the observation that the number of agent

contacts per day is age-dependent, peaking in mid-

dle age. Transmission between agents takes into con-

sideration the viral load of the infectious agent, the

infectivity factor of the COVID variant, a seasonality

factor, and the immunity of the susceptible agent.

In existing agent-based systems, the spatial loca-

tion of agents is typically modeled at a very coarse

level, such as presence in a household, school, or

workplace. Infection within a speciﬁc location is han-

dled by assuming that each agent has a certain num-

ber of contacts, and then these contacts are randomly

chosen from the agents present. One exception is (Is-

lam et al., 2022), where, similar to our work, they

model the detailed movement of agents in a plan map.

Instead of COVID in the workplace, they focus on

modeling student agents in an campus setting, evalu-

ating the placement of classroom seating to mitigate

the spread of COVID.

In the context of infectious disease work, we de-

ﬁne workplace hazard as the cumulative contact time

between all pairs of people. Contact is deﬁned in

terms of a conﬁgurable hazard radius. Risk is then the

pairwise transmission risk, as deﬁned by mathemati-

cal epidemiology. Actual county level public health

data determines the average disease burden (as a func-

tion of time) in the employees home county, and epi-

demiological modeling is used to measure transmis-

sion rates and other epidemiological parameters based

on these data. These parameters reﬂect the time vary-

ing policies and practices in each home county. With

this framework it is possible to compare the expected

hazard and risk any employee might face in any par-

ticular workday to the population based hazard and

risk measured for each home county. Furthermore,

the agent based simulation supports a quantitative as-

sessment of workplace practices put in place to reduce

occupational hazard and risk from SARS-CoV-2.

We present an agent-based simulation system that

estimates COVID-19 hazard and risk by recording

pairwise interactions between simulated employee

agents in the workplace. Simulated agents move

about a plan map view of the workplace, guided by

a calendaring service that sets the daily schedule for

each agent, which includes meetings, lunch, and cof-

fee and restroom breaks. The natural ofﬁce work

structure is re-created by placing agents in a vir-

tual organizational chart. Agents in the same orga-

nizational line have assigned ofﬁces next to one an-

other and will have scheduled meetings with one an-

other. As agents move about the workplace, our sys-

tem records hazard and risk when agents are within

a distance threshold. Epidemiological compartmental

modeling is used to seed some agents as infected, us-

ing transmission rates from their home county, and

then the workday simulation will record exposure

events to other susceptible agents.

Comparing our proposed system to existing agent-

based systems, the former tend to operate at a macro

level, modeling entire countries or metropolitan re-

gions (Kerr et al., 2021; Hinch et al., 2021; Shat-

tock et al., 2022). The location of agents and their

interactions happens at an abstract level, in census

block groups (Chang et al., 2021), statistical local ar-

eas (Chang et al., 2020) or even more abstracted as

”school” or ”workplace”. We focus on a particular

workplace site, adding a ﬂoor plan map and modeling

detailed (x,y) telemetry of agents in the ﬂoor plan.

This allows our system to model speciﬁc virus trans-

mission events at an exact location between the in-

fected and susceptible agents. We don’t need to pos-

tulate, as in the more generic agent-based approach,

general exposure risks when two agents are in the

same generic context like a school or household. Sec-

ondly, for interventions, this allows the exploration of

how modiﬁcations to the ﬂoor plan changes agents’

behavior and hence infection events. And ﬁnally, for

reporting, our system allows for visualizations based

on the ﬂoor plan, such as heat maps of exposure

events in the building. This reveals trouble spots in

the ﬂoor plan that may require tweaking to improve

agent / employee trafﬁc ﬂow.

In this paper, we use the agent-based simulation

system to quantitatively compare COVID-19 hazard

and risk for different workplace policies or interven-

tions. By plotting this risk as a function of building

occupancy, we can look for intersection points with

the same risk curve of the same agents working from

home. This crossover point suggests a safe operation

building occupancy, where workplace risk equals the

county-based working-from-home rate. We perform

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418

this analysis for two building policies and also look at

the effect that vaccinations have on the process.

2 METHODS

2.1 Epidemiology

2.1.1 Epidemiological Data

This study uses data from the USAFacts COVID-19

datasets (USAFacts, 2020) to measure the baseline,

time varying, disease hazard and risk in each employ-

ees home county. This data includes daily COVID-19

conﬁrmed cases and deaths, compiled by the CDC,

and obtained directly from state and local agencies.

For the two building interventions tested in detail,

all agent based simulation runs were done for a full

workday on the date July 30, 2021. Later, for a his-

torical analysis, the date range is opened up to a se-

ries of dates in 2021 and 2022; in principle, any series

of dates can be chosen. Where historic data exists,

county disease prevalence is taken from the historic

data. For a chosen 1-4 weeks into the future, county

disease prevalence would be predicted by epidemio-

logical modeling.

2.1.2 Epidemiological Model

To derive the time varying epidemiological parame-

ters from this data, we chose the SpatioTemporal Epi-

demiological Modeler (STEM) (Douglas et al., 2019;

Edlund et al., 2010), a modeling framework available

through the Eclipse Foundation (Kaufman, 2022).

The framework and model are open source and avail-

able under the Eclipse Public License (EPL2) (Alam-

oudi et al., 2020). STEM supports a variety of models

and provides a graphical model design tool for new

model composition (Baldassi et al., 2021). The par-

ticular model used in this study, the compartmental

model, is discussed in detail elsewhere (Gopalakrish-

nan et al., 2021b; Gopalakrishnan et al., 2021a). This

model demonstrates a statistical error (MAPE) of less

than 0.5% for predictions 1-4 weeks into the future.

It was run at least weekly for more than a year to ac-

curately predict ICU bed demand for Tampa General

Hospital (Gopalakrishnan et al., 2021b). As input to

the agent based simulation, the data from USAFacts

was used to determine the initial probability that em-

ployees residing in a given county arrived at work in

the infectious state. Since the worksite being mod-

eled is in Santa Clara County, the transmission rate

obtained from the epidemiological modeling of Santa

Clara on any particular date was used in the agent sim-

ulation. This transmission rate varied over time, re-

ﬂecting changes in local practices, behavior, and reg-

ulation (Gopalakrishnan et al., 2021b).

2.1.3 Model Calibration

The force of infection that drives new incidence in

most epidemiological compartment models has the

form

βSI/P (1)

where S is the susceptible population, I the infectious

population, P the total population, and β the transmis-

sion rate parameter (with typical units of 1/[person-

day]). On the other hand, the disease transmission

rate in a typical agent based model is stochastic and

depends on the cumulative number of contacts be-

tween agents. Contact implies pairs of agents gath-

ering within a hazard radius (deﬁned as 6 feet in this

model) with a smallest discrete time interval of 1.0

second. If two agents are within this deﬁned radius

for any period of time that is recorded as a hazard;

but it is only a risk if one of the agents is infectious

(shedding virus) and the other is susceptible. The

total number of exposed agents (those becoming in-

fected at work) depends on the cumulative contacts

in [person-seconds]. This is not a universal number

but depends on details of the workplace and agent be-

havior. To calibrate this stochastic transmission pro-

cess, the cumulative number of hazardous encoun-

ters was measured for the simulated workforce with

the building running at a normal capacity of 500 em-

ployees, and with no interventions in place. A single

calibration parameter was then set so that the num-

ber of newly exposed agents (the incidence) matches

that predicted for an equivalent population group in

Santa Clara on the same date. This calibration factor

was kept constant as other interventions and building

policies were varied across multiple runs of the Agent

Based Model.

2.2 Agent Based Modeling

In this section, we describe workplace modeling and

interventions, creation of agents and their calendars,

and our cloud-based simulation engine with user in-

terface dashboard.

2.2.1 Building Structure and Locations

The workplace used for the agent based simulation

was the IBM Almaden Research Center in San Jose,

California. CAD drawings of the physical site were

transformed into black and white bitmaps with a res-

olution of 0.454 [feet/pixel]. Fixed locations (pix-

els) representing destinations were assigned for all of-

Agent Simulation Using Path Telemetry for Modeling COVID-19 Workplace Hazard and Risk

419

ﬁces, labs, bathrooms, auditorium and cafeteria en-

trances, conference rooms, and facilities sites, along

with unique locations for all chairs in the cafeteria

and auditorium. The building itself was divided into

12 partitions or tiles representing the different wings

of the building at each ﬂoor. These partitions sup-

ported distribution of the simulation across multiple

cloud compute nodes.

2.2.2 Path Finding

To determine the routes or paths agents would take

during their daily activities in a simulation, a path

ﬁnder leveraging a Bi-directional A* algorithm was

employed. For each partition of the building, this path

ﬁnder was used to generate all possible combinations

of paths between each unique location. A path object

is represented in our system as a structure with the fol-

lowing properties: identiﬁer, starting and ending loca-

tion, the owning partition, and a list of steps or coordi-

nates comprising the path. These pre-computed paths

were persisted in a database to be referenced by the

simulation engine when constructing the plan needed

by an agent to get from point A to B. While paths

within partitions are pre-computed, paths across par-

titions were computed at run-time using breadth-ﬁrst

search across the connections deﬁned in the building

graph conﬁguration, where nodes represent a partition

and edges represent either stairs, elevators, or other

way-points between partitions. Random selection of

way-points was used to simulate agents making a de-

cision about the choice of way-point they would use

when crossing partition boundaries.

2.2.3 Employee Properties, Organization Chart,

and Home Address

Synthetic employees were created programmatically,

with a Poisson distribution on commute distance used

to deﬁne employees’ home addresses in nearby coun-

ties. An organizational chart was created with four

levels of technical management up to and including

the lab director (who reports to an offsite Director

of Research). Facilities staff have a similar reporting

structure under an offsite facilities director. Offsite

agents were not explicitly modeled in the simulation.

Each onsite employee and manager had a unique pri-

mary work location (e.g., ofﬁce) and secondary work

location (e.g., lab).

2.2.4 Employee Calendars

At the beginning of each workday, employee agents

arriving at the site were each assigned a unique cal-

endar of events with destination location and dura-

tion. These included work time intervals at primary

and secondary work locations, coffee breaks (with a

destination of the cafeteria), restroom breaks, meet-

ing at a colleagues ofﬁce, conferences, lunch breaks,

and all hands meetings. Colleagues meetings were

derived preferentially for using the org chart to favor

meetings within an organization (including meetings

between manager and employee). With all building

paths pre-computed (see above), path IDs were asso-

ciated with every employee calendar event based on

the start and destination locations for the event. The

calendar also included travel times to allow for transit

of a given path (although trafﬁc jams could result in a

delayed arrival at a meeting or event).

2.2.5 Trafﬁc Flow Model

Unobstructed, employees would move around the

building following pre-computed paths with an ini-

tial velocity of 4.54 feet/second. People (like cars)

can not move through one another. High densities are

known to reduce speed - eventually leading to traf-

ﬁc jams. We based our model of walking speed on

Newell’s optimal velocity (OV) model (Newell, 1961;

Wang et al., 2011), with velocity parameterised as a

logistic function in density and described by the fol-

lowing equation:

s =

1 + exp

k(n−n

)

(2)

Where s is the scaling factor used for reducing walk-

ing speed, k is the logistic growth rate, n is the num-

ber of nearby agents, and n

is the midpoint. Values

used for k and n

were 0.9 and 3.0 respectively. The

number of nearby agents, n, is determined by super-

imposing a mesh with 1.8×1.8 ft

cells over the plan

map, partitioning agents at each moment in time into

velocity groups.

2.2.6 Interventions and Building Policies

Although the workplace modeled was calibrated for

a typical occupancy of 500 employees onsite, the

building occupancy does vary widely with, at times,

over 700 employees (including summer interns), and

of course many fewer onsite employees during the

height of the pandemic. The number of onsite em-

ployees was varied (between 34-750) to study the ef-

fect of policy on disease hazard and risk. Two distinct

methods were used to select this number for a given

run: employees could be selected at random, or by

third line organization in the org chart. In this way

the org chart itself is used to model a particular social

network graph. Another variable used in the simula-

tion was the use (or non-use) of alternate entrances

to densely populated areas including the auditorium

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420

(one or two separate entrances), the cafeteria (one or

three cash registers), etc.

2.2.7 Disease Transmission, Initialization, and

Herd Immunity

At the start of each agent based simulation the ini-

tial infectious fraction is determined by public health

prevalence data for the home counties of all employ-

ees on the date to be simulated. In the agent based

simulation, a SEIR transmission process (Anderson

and May, 1992) is used so that a susceptible individual

in proximity to an infectious individual has the poten-

tial to move the susceptible individual to an exposed

state. In the exposed state individuals are incubating

the virus but not yet infectious. The incubation pe-

riod is chosen as one day, so that individuals exposed

at work return in the infectious state the next day.

To understand how vaccination and recovery from

prior infection is handled, ﬁrst consider that in epi-

demiological compartment modeling, recovered and

vaccinated individuals are often referred to as re-

moved, or in one or more R compartments. This is the

case because the force of infection depends only on

the fraction of individuals susceptible, S, and the frac-

tion infectious, I. Over time, waning immunity may

lead to removed individuals returning to a susceptible

state, but instantaneously they are not part of the force

of infection. This is also reﬂected in the deﬁnition of

the effective reproductive number (R

) which is a re-

scaling of the basic reproductive number (R

) by the

fraction of susceptible individuals. i.e.,

∼ R

(S/N),

where N is the total agent population. We take advan-

tage of this fact in our experimental design by initial-

izing the simulation beginning with all employees ei-

ther in a susceptible or infectious state, and generating

multiple runs as a function of onsite employee pop-

ulation. In so doing the results can be applied to any

level of initial herd immunity simply by re-scaling the

building population by the fractions susceptible. For

example, in a building with population of 1001 indi-

viduals (one infectious), if 50% are initially immune

(removed) due to previous infection or from vaccina-

tions, then the outcome of the simulation is mathe-

matically identical to a simulation run with 500 sus-

ceptible individuals (and a single infectious). Accord-

ingly, estimation of the removed population for any

simulation date can be performed as a post processing

step and the appropriately re-scaled population used

to predict hazard and risk on that date. This approach

will be explained in detail in the results and discus-

sion section 3.

2.2.8 Batch Runs

To examine a policy choice, one would like to run a

batch of agent simulations over a matrix of conﬁgu-

ration parameter values, saving recorded hazards and

risks as a function of the parameter matrix. When the

batch run of simulations is complete, we would tend

to favor a policy choice that minimizes the estimated

hazards and risks. Ideally, there is a base level of ac-

ceptability when the risk from working at the work-

place is approximately equal to the risk of working at

home over the same 8 hour work window.

We have built a batch run system to examine pol-

icy choices, where the batch run is speciﬁed by a set of

conﬁguration parameters to vary, plus the set of pos-

sible values. The batch system forms the outer prod-

uct of the parameter choices; for N parameters, we

form a N-D tensor of all the parameter combinations.

After forming the tensor, the batch system calls the

main simulation engine for each tensor cell, recording

the resulting hazards and risks in an event database.

Graphs and data analysis is performed by rolling up

results across parameter values.

2.2.9 Cloud Architecture

Fig. 1 shows our agent based simulation engine as de-

ployed on Red Hat OpenShift v4.6 in the IBM Cloud.

RedHat OpenShift is a platform as a service based on

Kubernetes (Vayghan et al., 2018) providing software

developers tools for creating and managing cloud na-

tive applications using Linux containerization tech-

nologies. Our cloud instance is comprised of 6 com-

pute nodes, with each node having 16 CPUs (Intel

Xeon CPU E5-2683 @ 2.00GHz) and 64 GB RAM.

The data for simulations, which included details

such as agent properties, building locations, disease

states, events, paths, etc. were stored as JSON doc-

uments in CouchDB (Manyam et al., 2012). The

database instances were conﬁgured in cluster mode,

having three replicas for high availability, and with

replication between instances enabled for redundancy.

Microservices providing Application Program-

ming Interfaces (APIs) in support of various functions

such as retrieving and modiﬁcation of data contained

within the CouchDB instances were developed with

LoopBack v4. LoopBack is an open-source frame-

work based on Node.js, Typescript, and OpenAPI

standards enabling developers to build APIs for ac-

cessing database backends and other web based ser-

vices quickly. Additionally, we deployed an API gate-

way based on aiohttp and Python 3.9 to provide a con-

solidated interface to the microservice APIs deployed

in our cluster.

The simulation engine was deployed as a set of

Agent Simulation Using Path Telemetry for Modeling COVID-19 Workplace Hazard and Risk

421

RedHat OpenShift on IBM Cloud

API Gateway

User Interface

Agents

Calendars

Diseases

Disease States

Hazard Events

Movement Events

Epidemiological Data

Locations

Paths

Databases

Configurations

Services

Agents

Calendars

Diseases

Events

Epidemiological

Locations

Paths

Configurations

Batching

Analytics

Simulation Engine

Coordinator

Workers

0 1 2 3

4 5 6 7

8 9 10 11

Figure 1: Agent based simulation engine deployed on RedHat OpenShift in the IBM Cloud.

containerized processes representing a coordinator

and a set of workers. These individual components

were developed with Python 3.9.9 using the aiohttp

package as the basis for the communication model.

The coordinator is responsible for keeping the simu-

lation date and time, controlling synchronization, and

reconciling the entering and exiting of agents between

workers. A worker process is deployed for each part

of the building or partition it represents. For our sim-

ulation of the IBM Almaden Research Center, we di-

vided the building into 12 distinct partitions. To sim-

ulate an alternative site would simply require deploy-

ing fewer or additional worker processes depending

on the layout of the building. Workers are responsi-

ble for computing their part of the simulation, which

includes steps such as handling new calendar events,

moving agents within and between partitions, prox-

imity detection, and disease transmission. These pro-

cesses would utilize the microservices mentioned pre-

viously to create and update simulation data such as

movement and hazard events and disease states for the

agents.

As mentioned previously, the coordinator controls

the overall ﬂow of the simulation. Its primary job is

to handle the synchronization of a tick of the clock. A

tick in our simulations is deﬁned as 5 seconds. Thus,

every call the coordinator makes to the workers to

progress will represent 5 seconds of elapsed time in

the simulated world. Furthermore, workers will per-

form a micro-tick analysis at 1 second intervals within

the 5 second tick for analyzing the movement, prox-

imity, and disease transmission of agents. This ﬁne-

grained timing allows our system to record very de-

tailed information regarding the progress of a simula-

tion.

Analytics based on the outcome of the simula-

tions can be queried and viewed as plotted images

and JSON output. The JSON output provides users

the capability to use the summarized results in their

own analytic or graphing tools. CouchDB views were

employed to transform the raw movement, hazard,

and agent disease state data into summarized results

after a completed work day. Fig. 2 shows an ex-

ample heatmap visualization of agent-to-agent expo-

sures (red) in one simulated day in the cafeteria dining

area of Almaden Research Center, outlined in dark

blue. Through this service an operations ofﬁcer has

the tools at hand to make data driven decisions and

apply policy actions depending on the outcomes.

Cafeteria Dining Area

Figure 2: Example heat map of COVID-19 exposures (red)

in one partition of Almaden Research Center, showing most

simulated exposures happen in the cafeteria dining area

(outlined in blue).

2.2.10 User Interface

To visualize the simulations, we developed a web-

based application based on React v17.0.2 and de-

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422

ployed in our OpenShift cluster along with our other

components and microservices. Fig. 3 shows an ex-

ample of our web application with the 2nd ﬂoor, D-

wing as the focus. The application provides the abil-

ity to see the entire layout of a building and view the

instantaneous locations of the agents. Depending on

their disease state, agents will either appear in one of

the possible 4 colors: blue for susceptible, red for in-

fected, yellow for exposed, and green for recovered or

vaccinated. The application provides users the abil-

ity to select the date and time period, as well as the

playback speed of a simulation. Our application also

provides additional ﬁltering capabilities for viewing

agents of selected states, selecting agents by their se-

rial number, and recorded exposures. Lastly, the web

application is integrated with our API gateway and

analytic services providing users a single purpose ap-

plication for working with simulations.

3 RESULTS AND DISCUSSION

From the data generated by the agent based simula-

tion it is possible to measure both the hazard and the

risk associated with transmission of the SARS-CoV-

2 virus. Hazard reﬂects the frequency and duration

of encounters between people within a conﬁgurable

hazard radius (6 feet in these simulations). It does

not depend upon - or presuppose - disease transmis-

sion. Transmission risk exists only when both sus-

ceptible and infectious individuals are in the building.

We note that other hazardous factors could be mod-

eled, and studied, but in the case of aerosol transmis-

sion of an infectious disease the proximity of people

to one another is fundamental to the hazard - and to

any interventions designed to remediate it.

3.1 Hazard Distribution

Figs. 4a-4d show the distribution of hazard exposure

as a function of number of employees in the building.

As deﬁned previously in section 2, the units of hazard

are [person-seconds]. The data is shown as a series

of violin plots, where each sub-ﬁgure represents the

outcome from a different run condition. In Fig. 4a,

on site employees are selected by third line organiza-

tion and alternate routes are disabled, while in Fig. 4b,

on site employees are selected by third line organiza-

tion and alternate routes are enabled. In Fig. 4c, on

site employees are selected at random and alternate

routes are disabled, and in Fig. 4d, on site employ-

ees are selected at random and alternate routes are en-

abled. Each violin represents one full day run of the

simulation using ﬁve different random number seeds.

In all cases the daily hazard exposure increases sys-

tematically with building occupancy.

The total work force hazard based on person-

person contact time is shown in Fig. 5. The units are

[person-seconds]. The standard deviation is obtained

by averaging the mean hazard for each distribution

over the ﬁve trials. For those run conditions where the

employee population is selected at random, the num-

ber of employees selected is exact and plotted along

the abscissa. Where on-site employees are selected

by the number of third line management organizations

allowed in the building, the number of employees will

vary with randomized trial as third line organizations

vary in size. This variation is shown as a horizontal

error bar for this mode of population selection. To

understand the vertical scale in Fig. 5, if the work-

force hazard is (for example) 150,000 [person-secs])

with 500 employees in the building, that corresponds

to an average person-person exposure of 300 person-

seconds of contact per employee over the 8 hour day.

Note that the measured hazard does not always fol-

low a simple linear relation with building occupancy.

In particular, for occupancy determined by selecting

third line organization(s), and with alternate routes

enabled, the measured hazard follows the hazard vs

number of employees for selection by third line orga-

nization(s), and without alternate routes, until a build-

ing population of 300 employees where there is a

knee in the data and hazard increases at a reduced rate

for alternate routes enabled (orange symbols).

In all cases the mean hazard-exposure increases

with building occupancy. Selecting employees by

third line organization leads to systematically higher

hazard than random selection. Supporting alternate

routes to reduce crowding systematically lowers haz-

ard exposure. The observed variation with run con-

ditions demonstrates that the occupational hazard de-

pends both on the the physical layout of the build-

ing as well as the social (or organizational) network

graph reﬂecting connections between people. Either

can be effectively modiﬁed by appropriate interven-

tions and the corresponding outcomes can be mea-

sured. Observe that for each run condition, the haz-

ard data was ﬁt with a linear least squares ﬁt with

respect to the number of employees, but in general

the observed hazard vs number of employees on-site

may not always be linear. This is particularly evident

for the runs where on-site employees were selected

by organization, and alternate routes were allowed.

Alternate routes are most effective in reducing haz-

ard when and if crowded conditions such as extended

cafeteria checkout lines are a signiﬁcant source of

person-person contact. This crowding is and of it-

self nonlinear, and the non-linearity is observed for

Agent Simulation Using Path Telemetry for Modeling COVID-19 Workplace Hazard and Risk

423

Figure 3: User interface for the agent based simulation engine showing a zoomed in view of a running simulation for the 2nd

ﬂoor D-wing of the building during lunch time.

(a) Employees selected by org, alt. routes disabled (b) Employees selected by org, alt. routes enabled

Figure 4: Violin plots showing the hazard exposure [person-seconds] distribution as a function of the number of onsite

employees. Each sub-panel corresponds to a different run condition. For all run conditions the average daily hazard increases

with building occupancy.

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Figure 5: The ﬁgure shows the total work force hazard

(person-person contact time [person-seconds]) as a func-

tion of the number of onsite employees. The data was ob-

tained by averaging the mean hazard (see Figs. 4a-4d) over

ﬁve runs with different random number seeds. In all cases

the employee-employee contact time increases with build-

ing occupancy. Selecting employees by third line organi-

zation leads to systematically higher hazard than random

selection. Supporting alternate routes to reduce crowding

systematically lowers hazard exposure.

relatively high building populations. This is to be ex-

pected given the non-linearity of trafﬁc ﬂow (and of

Newell’s optimal velocity model used in this simula-

tion (Newell, 1961; Wang et al., 2011)).

3.2 Risk of Disease Transmission

Figs. 6a-6d show the number of employees infected

as a function of time since midnight [hours] for four

run conditions. When infected, susceptible employ-

ees ﬁrst enter a latent exposed state, and become in-

fectious on the following day. The number of employ-

ees on site is selected by organization, or selected at

random; each with and without the use of alternate

routes. Each sub-ﬁgure shows a series of runs with

varying average number of employees on site (shown

in the legend). Each curve represents an average over

ﬁve runs with ﬁve random number seeds. The stan-

dard deviation is shown at the end of each workday. In

all cases, for all runs, the run duration was a one full

business day. The curves represent the average cumu-

lative sum of infections over the day. Each curve ter-

minates at a slightly different time based on the time

of the ﬁnal infection for that run condition.

Based on individual calendars, arrival times for

employees varies between 6:30am and 10am. The

rate of new infections (the slopes in Figs. 6a-6d)

starts at zero at 6:30am when the building is empty,

reaches a maximum around lunchtime where the

largest groups gather in the cafeteria, and falls off

again as people leave at the end of the day. Disease

transmission is a stochastic process and the number

of individuals exposed at work (and the time of day

for the exposures) varies from run to run. The dashed

lines represent the number of expected infections had

a sub-population of the same size remained at home.

Based on the cumulative disease exposures during

the workday, Fig. 7 shows the infection risk vs. the

number of employees in the building. The infection

risk is measured by the cumulative number of newly

infected (exposed) employees over the full workday.

The total risk is measured in ﬁve trials for the run

conditions shown in the legend. Once again, where

on-site employees are selected by third line organiza-

tions, the number of employees varies with random-

ized trial. This variation is shown as a horizontal error

bar for this mode of population selection. For each of

the run parameters (or mode) listed in the legend, we

also show the slope based on a least squares ﬁt to the

data. This slope represents the incremental increase

in infection risk as additional employees arrive in the

building.

In Fig. 7, in black, we plot the expected number of

new exposures for the same sub-population if the indi-

viduals remained in their home counties and not come

to work. This is derived from the county level SARS-

CoV-2 epidemiological modeling and prevalence data

scaled to the same sub-population size.

As discussed above, none of the results from the

agent based simulation are universal, since they are

a function of both building layout, workplace poli-

cies, and other interventions including the size of the

onsite workforce. However, for any particular work-

place or model workplace, it is possible to quantita-

tively compare the on-site risk to the corresponding

risk if the same sub-population of employees were to

remain at home. In Table 1 we list, for each mode,

the incremental increase in risk as a function of the

number of onsite employees (the slope in Fig. 7), as

well as the number of onsite employees at which the

total onsite risk is equivalent to the current at home

risk. This is the point at which the risk lines for on-

site employees crosses the average risk line for the

same sub-population at home. As is the case in Fig. 7,

the population size along the x-axis does not include

individuals in an immune or removed state, so if the

risk lines cross, the onsite population can be re-scaled.

For example, at 100 employees, and if 50% of em-

ployees are known to be fully vaccinated or otherwise

immune, then the risks become equivalent for 200 on

site employees. This crossing point does not represent

zero risk, it simply identiﬁes the onsite population and

policies, for a particular workplace site, where the av-

erage occupational risk would most closely match the

Agent Simulation Using Path Telemetry for Modeling COVID-19 Workplace Hazard and Risk

425

(a) Employees selected by org, alt. routes disabled (b) Employees selected by org, alt. routes enabled

Figure 6: Number of employees infected as a function of time of day [hours], and as a function of number of employees

on site, for four run conditions with on site employees selected by organization or at random, with and without the use of

alternate routes. Each subﬁgure shows the average number of onsite employees (averaging over 5 random trials, with std. dev.

shown at the end of each workday). The dashed lines represent the total number of expected infections during the eight hour

workday had a sub-population of the same size remained at home.

average at home risk. Deﬁning an acceptable occu-

pational risk is, of course, a matter of policy. A zero

risk criteria would never support even partial return to

work policy. One might choose an intermediate pol-

icy such that acceptable occupational risk should, on

average, be half the current at home risk. Modeling

can not select criteria, but given the criteria, modeling

can evaluate the interventions and policies required to

achieve the deﬁned goal.

To examine using the intersection of risk lines as

a policy recommendation to a workplace site man-

ager, we performed a historical analysis of our sim-

ulation system, looking at how the crossover point

moved over nine months of the COVID-19 pandemic

from July, 2021 to March, 2022. For each date, we

ran 25 simulations (5 capacities × 5 random seeds)

to produce a risk vs. number employees chart such as

Table 1: The incremental risk per person working onsite

(from Fig. 7) and the estimated building occupancy where

total onsite risk is equivalent to the current at home risk for

each mode or site policy.

Mode Incr. Bldg.

risk per Occ.

person (+/- 5)

Random, with alt. routes 0.022 178

Random, no alt. routes 0.035 172

By 3rd line, with alt. routes 0.019 0

By 3rd line, no alt. routes 0.032 85

Fig. 7. Following the lowest risk policy choice from

our prior analysis, the simulations reduce agent popu-

lations randomly and alternate routes are enabled, so

we are focused on risk vs. number employees at each

date. For each chart, we estimated the best ﬁt lines

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426

Table 2: Historical analysis of crossover capacity during the Delta and Omicron waves. For nine dates from July, 2021

through March, 2022, we repeated the risk crossover analysis of Fig. 7 to estimate the recommended site capacity at IBM

Almaden Research Center. The recommended site capacity is lowest at the peaks of the Delta and Omicron COVID-19 peaks,

highlighted in red and blue.

Date (10

of each month)

2021 2022

Delta Omicron

Jul Aug Sep Oct Nov Dec Jan Feb Mar

Crossover

Capacity

155 142 157 180 168 177 130 154 157

to: 1) estimated risk, and 2) expected risk, and we

found the intersection point where the risk levels cross

one another, which can be taken as a recommended

workplace site capacity. In Table 2, we show the rec-

ommended capacities for these nine dates, the 10

of the month from July, 2021 through March, 2022,

which includes both the Delta and Omicron COVID-

19 peaks in the US (highlighted as red and blue in Ta-

ble 2). As we were hoping to see, the recommended

capacity drops to its lowest points at the peaks of the

Delta and Omicron waves.

4 CONCLUSION

To advise workplace site managers on handling

hazard and risks from infectious diseases such as

COVID-19, ideally one would like to explore the

effects of different policies using a data-driven ap-

Figure 7: The ﬁgure shows the infection risk as measured

by the cumulative number of infected employees over one

workday as a function of the number of employees in the

building. The error bars reﬂect the standard deviation over

ﬁve trials with different random number seeds. Each line

represents a different set of run conditions as indicated in

the legend. The black data show the expected number of

new infections (based on the county level epidemiological

data) had the same sub-population stayed at home.

proach. Agent simulation provides a lens for explor-

ing policy choices by systematically altering simula-

tion parameters. The differing simulation parameters

changes the physical interactions between virtual em-

ployees traversing a virtual workplace, yielding dif-

ferent levels of hazard and risk. In a simulation of a

large research laboratory with maximum capacity of

750, we compared the effects of reducing the popu-

lation by randomly selecting employees in the orga-

nization chart with eliminating some number of third

line organizations. We also explored simulations with

and without the beneﬁts of alternate routes available

to the agents for social distancing (e.g. multiple cash

registers, multiple auditorium entrances). Comparing

the hazards and risks from these options, we showed

that the random selection method was the best, and

that alternate routes do result in lower virus transmis-

sion. For the various parameter choices, we can plot

hazard and risk for different levels of building occu-

pancy, and we estimate the number of employees who

can ”safely” work in the building. Here, ”safe” is the

point where workplace virus risk is the same as work-

ing at home, which is estimated by county epidemi-

ological modeling. Even if one wants to operate at

a stricter level of safety, the agent simulation frame-

work is general enough to provide valuable guidance

to a workplace site manager.

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