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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Multi-paradigm Methodology for Enterprise Modelling using Agent-based Modelling and System Dynamics</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Dushyanthi Mulpuru</string-name>
          <email>dushyanthi.mulpuru@tcs.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Abhishek Yadav</string-name>
          <email>y.abhishek1@tcs.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Anwesha Basu</string-name>
          <email>anwesha.basu1@tcs.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Tata Consultancy Services Research</institution>
          ,
          <addr-line>Pune 411013</addr-line>
          ,
          <country country="IN">India</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The Covid-19 pandemic has significantly altered business operating models. Enterprise decision makers responsible for devising actionable business operational strategies are confronted with making informed decisions in the state of continuously evolving pandemic landscape. As pandemic concerns subside, their objective is to formulate a workplace opening strategy that mitigates employee infections and the subsequent impact on project delivery. It is therefore critical to appropriately model the underlying aspects of the enterprise system and enable strategy evaluation. Enterprise in this context represents a complex, dynamic system composed of multiple sub-systems with varying characteristics, levels of uncertainty, granularity, data availability and scale. Owing to these distinctions, diferent modelling paradigms are better suited to individually model these sub-systems, and their integration results in a comprehensive model that is a close approximation of the real system. This paper presents a hybrid/multiparadigm approach for modelling the enterprise ecosystem, by building on the established concepts of Agent Based Modelling (ABM) and System Dynamics (SD) that enables evaluating the impact of operational strategies on employee infections. The model is formulated as integration of multiple subsystems and their interactions - infection module, employee and dependent, ofice infrastructure and society modules. These four dimensions, comprising the enterprise ecosystem, significantly influence the employee infection dynamics. While the SD model quantifies the aggregated infection dynamics of society at the population scale, ABM models fine-grained specifics of employees, dependents, infrastructure, and the resulting infection dynamics.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Agent-based modelling</kwd>
        <kwd>System dynamics</kwd>
        <kwd>Enterprise multi-modelling</kwd>
        <kwd>Model development</kwd>
        <kwd>Covid-19</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        The Covid-19 pandemic has greatly influenced the way businesses operate, with a major shift
in the employee operating model as employees transitioned to working from home (WFH) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
As enterprises formulate post-pandemic workplace strategies, their objective is to 1. Determine
the appropriate operating strategy to minimize the infection risk among employees as they
transition back to working from ofices (WFO). This includes establishing phase wise transition
timelines and enforcing suitable procedural and infrastructural restrictions. Since the influence
of the pandemic is not uniform across geographies, businesses operating in multiple geographies
must devise custom strategies. 2. Establish business continuity plan (BCP) to address the impact
of infections on the employees. The impact of pandemic on an employee can be two-fold.
a. Employee infection and b. Infection among dependents/household members. Employees
who have been impacted are unavailable to work, and the period of unavailability may vary
depending on the severity and must be factored into the project planning process.
      </p>
      <p>Building on this context, an enterprise can be conceptualized as an ecosystem composed
of - physical enterprise infrastructure, employee characteristics and their social behavior,
dependent characteristics, virus variants and their infection characteristics, and related policies
and interventions. An enterprise workplace/infrastructure/ofice is a collection of physically
inter-connected facilities. Employee characteristics on the other hand, include demographic,
project, health, and pandemic-related factors such as vaccination and infection history, whereas
behavioral characteristics include contact behaviors within diferent social contexts, such as
interactions with other employees within the workplace, with dependents living in the household,
as well as with other individuals of the society/geography. Enforced policies (e.g., limiting ofice
visits) and infrastructural constraints (restricting operating capacities of various infrastructure
facilities) significantly impact the behavioral patterns thereby influencing the infection spread
among employees. Additionally, infection trends prevalent within society/geography (they vary
significantly across geographies due to variations in the predominant virus variant, infection
rates, demographic diferences, pandemic strategies adopted, movement behaviors, and so on),
virus characteristics (infectivity rate), and infections within household influence employee
infections. The severity of infection in an infected individual varies based on the fatality rate of
virus, demographic factors (age, gender, comorbidity), individual’s infection history, vaccination
status (not vaccinated, partially, fully vaccinated), and eficacy of vaccine. Models intended for
supporting decision making on employee and enterprise working models should holistically
capture all the above-mentioned factors that contribute towards employee infections to evaluate
inter-dependencies of various interventions with the outcomes.</p>
      <p>
        Modelling has been extensively used in determining infection mitigation strategies [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]
presented an overview of various mathematical models such as compartment, statistical, and
machine learning models proposed in the literature for analyzing the infection spread and
prediction. Well-known compartment models based on diferential equations such as SIR (Susceptible
Infected Recovered), SEIR (Susceptible Exposed Infected Recovered) [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] assume a homogeneous
population, and work well in scenarios where infection dynamics needs to be understood at the
population scale. Modelling specialized contexts like workplaces requires capturing
heterogeneity in terms of characteristics and behaviour at the individual level, where aggregated models
are deemed ineficient. AI (artificial intelligence) forecasts of the infection spread on the other
hand, are not yet very accurate [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] due to constraints imposed by lack of adequate and accurate
data, and the algorithmic dynamics that rely heavily on the past behavior. Overcoming these
limitations, several studies ([
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]) used ABM to model individualistic characteristics
and behavior in varying contexts such as city, country and provided support to evaluate various
intervention strategies for mitigating infections. However, scalability is an issue - they either
require high-performance computing services, as in [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] or need to scale down the population to
make the simulation manageable, as in [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. ([
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]) despite having richer models, are limited to
modelling a specific geography/city and can only scale to tens of thousands of agents. ([
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ])
used multi-paradigm approach to overcome the limitations of individual paradigms. [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] starts
with an agent-based approach and once global structures emerge, switches to an equation-based
aggregated approach, mitigating scalability issues. However, this aggregation is not well suited
for analyzing the efects on the individual level, as the local interactions are only considered
up until the switching point, whereas [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] combines age-stratified and location-specific SEIR
models in an ABM framework to capture virus transmission dynamics aggregated by age cohort
in diferent geographies. ([
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], [13]) modelled risk of infection transmission in
workplace/facilities. [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ] used a combination of microexposure and probabilistic modeling to estimate the
infection risk. But, employee infection risk from society is grossly simplified making it less
suitable for modelling distinct geographies of organization spread. [13] used ABM to evaluate
transmission risks in facilities but is computationally expensive due to model’s reliance on
stochastic lattice-based movements. Also, heterogeneity in workplace infrastructure as well as
infection risk from society are not accounted for.
      </p>
      <p>Modelling practices in general model the entire system using a single paradigm by
decomposing the entire system into sub-systems, thereby constraining the models to a specific level
of granularity. Multi-paradigm modelling on the other hand, allows for the representation of
interactions between elements at diferent granularities [ 14]. [15] highlights the importance of
modelling objectives in determining the nature of the model, as diferent modelling objectives
lead to diferent models within same problem situation. Modelling objectives in conjunction
with problem structure and data availability helps identifying the levels of granularity that can
serve as a basis for determining the appropriate modelling approach. ABM is a logical choice
for fine-grained modelling of ofice infrastructure, employee, dependent and virus models due
to the availability of data and its ability to express heterogeneity and support for micro-level
interventions for studying emergent behaviour; however, detailed modelling of employee’s
societal interactions requires modelling the entire society/geography and poses challenges in
terms of citizen data availability and model scalability - as modelling citizens in their entirety for
multiple geographies (since employees are spread across geographies) becomes computationally
expensive, and hence calls for an aggregated modelling using SD. The ecosystem model should
therefore - 1. Capture the uncertain and dynamic nature of social system owing to the influences
of structural, regulatory, virus factors and 2. Allow for development of integrated models
without undermining the model predictions. Our contribution in this regard is a method for
modelling enterprise ecosystem to infer infection dynamics of employee and their dependents
within the organization by a multi-modelling paradigm, comprising of, a coarse-grained system
dynamics approach, and a fine-grained agent-based model. The proposed approach overcomes
the issues of data availability and scale while still allowing for a fine-grained representation of
the system of focus; and supports micro-level strategy evaluation.</p>
      <p>The paper outline is as follows-Section 2 visits the concepts of Agent Based Modelling and
System Dynamics, their contrasting capabilities, and explores hybrid SD-ABM architectures for
model integration. Section 3 formulates the enterprise ecosystem from the modelling perspective
and details the model construction process, describes integration approach and summarizes the
results. Section 4 concludes the paper and lays the direction for future work.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Background</title>
      <p>Agent Based Modelling (ABM) and System Dynamics (SD) are two widely used paradigms for
modelling complex dynamic systems in variety of problem domains [16]. They have diferent
concepts for representing the structure/behavior and hold some fundamental assumptions about
the system. This section describes the key concepts and characteristics of ABM and SD and
their integration approaches.</p>
      <sec id="sec-2-1">
        <title>2.1. Agent Based Modelling</title>
        <p>(a) Agent Based Modeling Concepts
(b) System Dynamics Concepts</p>
        <p>ABM belongs to the class of models in which a system is modelled as a set of interacting
autonomous agents having corresponding state and associated behavior. The global behavior of
the system emerges through the interaction of agents with each other and with their environment
[17]. Figure 1a outlines the key concepts of ABM. Agent is the primitive unit of computation
having its own well-defined Behavior as set of rules. An agent’s behavior can create/destroy
agents, and may trigger change in its own state/attribute or in the environment. The behavior
can either be timed or reactive. Timed behaviours are executed by the agent in a timely manner,
these behaviours are completely autonomous and can be executed across varying temporal
scales for diferent classes of agents while Reactive behaviours are usually triggered when one
agent interacts with another using message passing. Non–Agents (refer Object in the figure 1a)
lack autonomous behaviour but function as helper classes to perform computations that are
not agent specific. Environment houses all agents and non-agents and the agent’s actions are
constrained by the environment boundary.</p>
        <p>ABM owing to its flexibility to obtain a richer model to achieve high degree of realism and
capturing emergent phenomenon makes it an excellent choice to model and simulate complex
system-of-systems. Applications of ABM include modelling complex organizational and social
systems [17] in a bottom-up manner using domain knowledge and detailed information about
micro-behaviours of entities (e.g., citizen, employee etc.) in the system (e.g., building, city,
factories etc.) and global behaviour of the system which is unknown, emerges from the action
and interaction of agents. This modeling technique is best suited in scenarios where the system
is characterized by complex, nonlinear, discrete interactions between heterogeneous agents,
macro/global behavior of the system is not well understood (or) the aggregated dynamics cannot
be easily represented through equations and characteristics, but behavior at individual level
is known. However, scalability of the agent-based simulation is an inherent limitation, and
the high computational requirements yet remains a problem when it comes to modelling large
systems. ABM models being purpose specific, needs to be built at the right level of description
[17]; which makes it ill-suited for scenarios where micro level details are largely unknown.</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. System Dynamics</title>
        <p>SD ([18], [19]) is a top-down modelling approach where the system is modelled at the
macrolevel to analyze the changes in the system over time. The system’s dynamic behavior and
interactions are represented by a set of diferential equations, and realized using
machinesimulatable stock and flow models. Figure 1b depicts the central concepts of SD. Stock is a
fundamental unit that represents accumulation of a real-world entity. The value of a stock
represents the state/snapshot of a system at any point in time. Source and Sink are types
of stocks hypothesized to have infinite capacity. Flow, characterized by feedback and delay,
denotes the rate at which the entities in the connected stock change their state and is controlled
by the valve, which may be dependent on other values that are fixed (represented as Constant)
or values that need to be computed just-in-time (represented as Variable). Both constants and
variables are collectively referred to as Auxiliary variable.</p>
        <p>SD characterized by feedback structures with non-linearity, makes it well suited for
understanding the dynamic behavior of complex systems. It provides a macro-perspective and helps
understand the overall structure behind complex phenomena. It is widely used to analyze a
range of systems [20] and can be used with little or no data as inter-dependencies of the system
elements can be incorporated based on the domain expertise. SD is best suited in scenarios
where the overall system behaviour is well understood and can be reproduced as a series of
feedback loops, and where the focus is on the dynamics at the population level. It is less suited
for scenarios where the behavior of individual heterogeneous entities is the key focus of interest
since it cannot explain the micro behaviors in a system.</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Hybrid SD-ABM Modelling</title>
        <p>The complex, multifaceted systems pose considerable challenges for traditional,
singlemethodology simulation approaches [21]. Oftentimes, underlying sub-systems feature varying
levels of granularity, uncertainty, and are further limited by data availability. In such cases,
integrated modelling approaches are the most appropriate, wherein the system components are
modelled using the corresponding paradigms that suit them best. Using too many paradigms, on
the other hand, may introduce new complexities [14] and hence the advantages of employing
multiple paradigms must be balanced against the overhead of integrating them. The choice of
hybrid architecture is dependent on the interdependencies of the system components. Several
studies attempted to integrate the SD and ABM models and proposed various hybrid SD-ABM
architectures for the same. ([22], [23], [24]) presented an overview of the existing theoretical
guidance/frameworks on integrating SD and ABM. [21] proposed three broad classes of hybrid
SD-ABM integration based on [25]. These are referred to as interfaced, integrated and sequential
hybrid designs which difer depending on how either of the SD or ABM single paradigm
metamodels interact to produce the model’s output. In the sequential class, one simulation paradigm
capable of producing the required input for the second simulation is initially executed, and its
output is fed as input to the next paradigm. Communication between the paradigms is thus
restricted to a single point of time and output of the final model represents the outcome of the
overall model. The integrated class incorporates feedback between the paradigms representing
a continuous input exchange. The interfaced class, on the other hand, consists of non-sequential
execution of paradigms that combine their independent results to form the model outcome
without influencing each other. Hybrid SD-ABM architectures have found use in modelling
complex systems across diverse range of application areas such as health care, supply chains,
environment, and ecology.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Model Construction</title>
      <p>This section details the components of the enterprise system, identifies the scope and
characteristics of each module that helps the modeler determine suitable technique for model specification,
discusses the model integration approach, validation and results.</p>
      <p>Figure 2 depicts the conceptual model of an organizational structure. An organization operates
in diferent geographies that are decomposed hierarchically. An organization is composed
of multiple business units that execute multiple projects from various ofices belonging to
branches spread across geographies. Employee is based out of one of the ofices. Employees
and dependents represent an organization family residing in a household in the corresponding
geographical location.</p>
      <p>The overall ecosystem can be characterized as combination of systems that influence infection
spread among organization’s employees. Employee exposure to infection, as illustrated in Figure
4, is determined by individual employee movement behavior within the bounded ecosystem
(household + ofice) and aggregated societal behavior at the geographical population level
(society). These in turn, are highly influenced by regulatory framework (restrictions within
ofice movement/lock downs in society) and virus characteristics (prevalence of diferent mutants
with varying infectivity). The spread of employees across distinct geographies adds further
complexity as each geography has diferent seroprevalence levels, diferent rates of infection
spread and medical infrastructure that needs to be modelled. The system is decomposed into 4
interacting sub-systems. 1. Infection model 2. Employee model 3. Ofice Infrastructure model
and 4. Society model. The purpose, scope, granularity associated with each of the individual
components of the model along with details about experimental factors (levers/configurations),
assumptions, and choice of modelling is elucidated in subsequent subsections. This resultant
conceptual model forms a basis for developing a simulatable computer model that serves as
an aid to decision making within the specified context. Figure 3 outlines the schematic of the
enterprise specific Input data model. Output data model constitutes infections trends (Active,
Cumulative, Daily) within employees and dependents at various places (E.g. infection from
home, ofice, and society induced infections, respectively). Traversing the employee relationship
structure helps to understand the infection trends at various levels (such as ofice, transport,
project, business unit, branch, geography, and so on).</p>
      <sec id="sec-3-1">
        <title>3.1. Infection Model</title>
        <p>Susceptible-Exposed-Infectious-Removed (SEIR) model [26] is a well-known epidemic model to
predict the dynamics of infectious disease. Broadly, an epidemiological SEIR model represents
the following sequential phases of infection in a population: Susceptible (S), Exposed (E),
Infectious (I), and Removed (R). Multiple variations of SEIR models exist in literature that
account for factors such as birth, death, loss of immunity, vaccination, and reinfection and
are usually applied on population scale. Our approach captures the epidemiological spread
characteristics and evaluates its efect 1. On employees at the individual level using ABM to
account for the individual demographic, health and vaccination factors that can significantly
alter the infection progression of a person (employee/dependent), and 2. On the population
scale using SD to model societal transmission and thus factor its efect on the employee. This
section details the treatment of SEIR at an individual context modelled using ABM. Infection
model considerations at the population level is covered further in detail in section 3.4.</p>
        <p>
          The ABM Infection Model represents the infection progression in employees and dependents,
accounting for the following infection states - Susceptible (S), Exposed (E), Asymptomatic (AI),
Mild Symptomatic (MI), Severe Symptomatic (SI), Recovered (R), Dead (D). As depicted in the
ifgure 4, the transition from S to E is the result of combination of 1. Infection incurred through
contacts from society - represented by s2e (Susceptible to Exposed) rate, which is the probability
that a susceptible person in a given geography gets exposed to virus on a given day. This
is resultant of aggregated dynamics at a geography level within the society model explained
in detail in section 3.4. 2. Contact through behavioral interactions within household and
employee specific interactions with other employees within the ofice and transport, all of
which are obtained from the employee and the ofice model (section 3.2, 3.3). Remainder of the
transitions barring R to S depend on well-established state transition probability model which
includes individual demographic (age, gender), and health characteristics (immunization status,
comorbidity - diabetes, hypertension, chronic obstructive pulmonary disease (COPD)) from
the Employee model, virus characteristics (infectivity, severity and fatality, vaccination bypass
probability, recovery period, incubation period, transition probability between various states
and the associated delays) of all variants of interests and Vaccine type administered. Table 1 of
[
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] can be referred for detailed information of the same. Individuals with diferent co-morbidity,
vaccination and demographic values respond to virus diferently. R to S transition is simply
determined by the likelihood of reinfection and a specified time delay.
        </p>
        <p>The resulting model indicates the infection state of an employee or dependent at any given
time. Employee’s infection state further influences their ofice and home movement
behaviors within the employee model as they transmit infection during the incubation period and
self-isolate upon infection. ABM is the obvious choice for modelling this phenomenon as
it best models the micro-level individualistic characteristics and behavior. In the absence of
comorbidity information, country-specific age group-gender specific comorbidity distributions
are considered.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Employee Model</title>
        <p>The Employee model (Figure 5) represents the individual characteristics and behavior of the
employee which includes movement and interaction in a bounded environment (ofice, home)
over the course of the day. This estimates the impact of infection on the employee and helps to
suitably plan the business continuity to account for the absence. Employees and their dependents
are modelled as agents with distinct demographic and health profile residing in a prototypical
household in the geography of the ofice location. State of each anonymized employee include
demographic information (age, gender, city), project details (operating unit, business unit,
branch), ofice details (building, seat), health profile/comorbidity (hypertension, diabetic, COPD
and no history), infection state (S, E, AI, MI, SI, R and D), vaccination information (vaccine type,
date of vaccination, vaccination status - not vaccinated, partially vaccinated, fully vaccinated),
current location information (home, ofice, ofice transport (bus, cab)/private transport). The
dependent state comprises of demographic characteristics, health profile, vaccination details
and infection status. Employee vaccination is included in the model and vaccination rate follows
the city vaccination rate.</p>
        <p>On an average day, an employee interacts with 1. Dependents within the household 2. Other
employees within the ofice premises and during work commute in ofice provided transport
3. Other individuals in society outside work hours. These interactions serve as avenues for
employee infections. Of all the 3 kinds of employee interactions listed, only the household
and ofice interactions are modelled at the individual level. The approximated efect of societal
interactions is estimated using an aggregated society model (section 3.4). Determining the
consequence of infrastructure policy interventions on an individual employee level establishes
the need for an intricately detailed model of the employee interactions in the ofice, transport and
in the household environment (as employees who get infected in household spreads infection
in ofice). In the presence of detailed information and while the model does not result in
computational overhead, ABM is a logical choice for representing diverse range of individualistic
characteristics and behaviors and allows for encoding various influences on the individual level.</p>
        <p>On a given day, employee visits ofice basis eligibility constraints (e.g., fully vaccinated,
partially vaccinated, age group, should not be currently infected and so on). Timed behavior,
such as going to and leaving the ofice is modelled as a fixed routine-based movement, while
movement within the ofice and at home is modelled as random movement. Within the ofice,
employees move in close proximity to their desks in addition to utilizing various infrastructure
facilities described in section 3.3. The probability that the employee utilizes a facility at a given
time during ofice hours is a function of - hourly probability of employee visiting that facility, the
facility’s current operating capacity vs. the allowed operating capacity, and the visit frequency
allowed vs. number of visits made during the day. All these movements result in contact with
other employees. Infection within a place is sampled based on carpet area, susceptible and
infected head count in that place. This sampling provides the expected count of infections that
can occur within the specific duration, and the employees are appropriately infected. Infection
in an open place is modelled distinct to that of closed places as movement within open places
is mostly localized regardless of the carpet area, and infection does not depend on overall
population density but only on contact with a subset of employees. Additionally, employees
interact with household members outside ofice hours. Contact dynamics within household and
transport are modelled similar to that of a closed facility.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Ofice Model</title>
        <p>The ofice model captures a detailed representation of the ofice infrastructure as outlined
in Figure 6 using ABM to allow for policy-oriented what-if scenario analysis. Coupling this
model with infection and employee models helps analyzing ofice induced employee infection
patterns under varying infrastructural configurations. Ofice is a physical entity characterized
by operating hours (opening and closing time), workdays, location details (city, branch) and is
composed of various facilities categorized as Open (characterized by large carpet areas) and
Closed facilities. Each facility is characterized by seating capacity, carpet area, allowed capacity,
current occupancy and number of visits allowed per employee. Sector, Lab, Canteen, Gym, Rest
Room, Auditorium constitutes open facility whereas Pantry, Training Room, Meeting Room,
and Cabins are closed facilities. The facilities are equipped with a safe desk layout to ensure
social distancing.</p>
        <p>These facilities are utilized by the employees at varying times and with varying frequency
bounded by the imposed infrastructural constraints (capacity restrictions, visit frequency
allowed, and open/close patterns) resulting in varying infection spread. The structural decisions
imposed on this model efects the employee behavior patterns and influence the overall
system’s behavior. The count of ofice-induced infections is afected by several policy-oriented
configurable factors including 1. Percentage of workers doing WFO on any given day based on
ofice capacity restrictions and employee eligibility to go to work 2. Infrastructural layout (safe
desk layout), and 3. Workplace facility use policy (restraining allowed occupancy, operational
hours, and visit frequency) and ABM is an ideal choice for detailed representation of multiple
such ofices. Diferent infection trends emerge when few places are closed or operate with
limited capacity. The hierarchical decomposition of the infrastructure helps in the trend analysis
of ofice induced infections starting from a particular instance of any facility of an ofice up
until the organizational level. The dynamics are computed on an hourly basis to understand
the infection spread within ofice premises. Ofice infrastructure also includes transportation
Cab and Bus characterized by total seating capacity, capacity allowed, current capacity and is
availed by a portion of employees for ofice commute.</p>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Society Model</title>
        <p>The goal of modelling the society is to analyze the employee and dependent infections induced
by societal interactions. Although modelling the entire society/geography in a bottom-up
manner using ABM is a possibility; however, micro-level modelling of societal interactions
and infection dynamics at the geographical scale is infeasible due to 1. Unavailability of data
- model construction requires detailed demographic, health details, and the complete nature
of interactions of the entire population as highlighted in section 3.1, which is impossible to
obtain. 2. Computationally expensive to scale such models in the presence of large number of
geographies. Furthermore, the micro-level behavior of individuals within a society is out of
scope of analysis and simplifying the model to capture aggregated behavior does not compromise
overall model accuracy as long as the efects of aggregation are appropriately factored in the
overall model. These factors narrow down the model’s purpose to capturing citizen’s virus
exposure probability as a result of exposure rate of a given geography/current rate at which the
locality is exposed to virus represented using Susceptible to Exposed (s2e) rate, which is then
fed into the ABM model as depicted in figure 4 (contact from society)</p>
        <p>Figure 7 depicts a configurable stock and flow model representing the proposed aggregated
society model. It is a modified version of the classic SEIR model introduced in section 3.1 while
including the efects of vaccination. Six sequential cohorts - Susceptible ( ), Exposed ( ),
Infected ( ), Critical ( ), Recovered () and Deceased () represents the infection phases,
and an additional feedback loop from Recovered to Susceptible represents loss of immunity
and possibility of reinfection. Cohorts are represented using Stocks, and aggregated population
movement from one cohort to another is represented using Flows (indicated with ). Flows
are governed by a set of factors, which are represented as auxiliary variables, and time delays
(indicated using  ). Transition of individuals among these states depends on factors including,
but not limited to probability of contact with other infected individuals, transmission probability,
and virus characteristics like incubation period, infectivity rate, recovery rate, fatality rate,
reinfection rate, reduction in critical and fatality rates post vaccination, and transition delays.
The flows 3 ( to  ), 4 ( to ), 5 ( to ), 6 ( to ) depend on vaccine
adoption and vaccine eficacy. The concepts of vaccine (and booster dose) adoption and its
impact on infection dynamics is comprehended using another simplistic interconnected stock
and model containing three stocks: Eligible (), Vaccinated ( ) and population who are
Waiting ( ) for the next dose. This model infers the proportion of population in a geography
that – a) is vaccinated recently and possibly has high vaccine induced immunity () and b)
was vaccinated long back and possibly has less vaccine induced immunity (). These values
in turn, are utilized by the infection model.  is the probability of coming in contact with
infected people (the ratio of infected people contributing to infection spread, to the total living
population) and parameter  is a multiplier we use to tune this probability. Components of the
proposed stock and flow model are described in detail in [27].</p>
        <p>The model is first contextualized using available infection data (including, but not limited
to, locality specific net initial population ( 0), reported critical cases (0), reported deceased
count (0), detected active cases (0), detected recoveries (0), and tentative susceptible
percentage () obtained by querying public databases, census records, government
dashboards, authentic media bulletins, and published sero-prevalence surveys. We then estimate
parameter  by simulating the model with diferent  values and comparing simulated trends
of detected infected cases ( ), detected recovered cases (), critical cases ( ) and number
of deceased () with the actual trends.  is adjusted for prospective future scenarios, such
as best case scenario, scenario for complete movement relaxation, emergence of new variant
with higher infectivity than known variants. Finally, the 2 rates are computed for all possible
scenarios using 2 equation : 2 =  × . This process is repeated for all the geographies of
interest and the combined s2e data is then introduced into the ABM to account for the society
induced employee infection as indicated in figure 4, and the infection progression follows the
process described in the section 3.1.</p>
      </sec>
      <sec id="sec-3-5">
        <title>3.5. Model Integration</title>
        <p>Diferent classes of hybrid architectures were explored in Section 2.3. The proposed approach
(Figure 8) adopts a sequential mode since there is no bi-directional interaction between SD and
ABM models and it is suficient to model the aggregated societal infection dynamics
independently using SD and communicate its output to the fine-grained ABM model by establishing a
single point of data exchange between the two models.</p>
        <p>Initially the society module that is external to the ABM is modelled using Stock and Flow.
Aggregated infection statistics from various authentic sources as indicated in 3.4 are extracted
and transformed using an automated process. Multiple instances of SD model are then run,
one for each geography of interest over a configured time-period. The combined results of
all the individual instances are collectively utilized by the ABM as input parameters. Prior to
doing so, a transformation/decay function is used to account for the impedance mismatch (if it
exists) which is the diference in the movement pattern adopted by categories of employees to
safeguard themselves during an infection surge in the society. For example, in the case of IT
(Information Technology) enterprises where the job profiles do not demand high movement
behavior, this safe/reduced movement pattern follows exponential growth to peak infections,
followed by exponential decay. The ofice, employee, dependent, and the infection modules are
modelled using ABM and appropriate interventions are introduced using Intervention Injector to
evaluate the impact of various candidate interventions. The ABM is then run, taking as input the
enterprise specific employee and infrastructural data represented in figure 3, contextual/domain
(a) Ofice induced active infections
(b) Ofice induced cumulative infections
data (virus and vaccine characteristics), intervention parameters along with the output of the
impedance mismatch function. The output of the ABM represents the final output of the
hybrid model. Various KPIs (Key Performance Indicators) displayed during the simulation using
simulation dashboard are then stored into file/database for any further analysis.</p>
      </sec>
      <sec id="sec-3-6">
        <title>3.6. Validation and Results</title>
        <p>The proposed approach is validated on a large organization (425K+ employees living with 600K+
registered dependents) with multiple ofices spanning multiple geographies (140+ ofices across
30+ branches) by running the simulation model with enterprise-specific data (anonymized
employee, dependent, and ofice infrastructure details). History of previous infections served as
validation data. The simulation is configured to run over a time period in the past (January to
June 2021) for which actual reported data is available, and the simulation results are compared to
establish the operational validity of the model. Following validation, several experiments with
varying scenarios were carried out to better understand the future infection risk of employees
and dependents, thereby impact on the project delivery from opening of ofices under varying
interventions. Figure 9 depicts the infection trends of a few selected optimistic scenarios under
various ofice operating capacities (25%, 50%) and transition timelines (March, April 2022)
with similar micro-level interventions (canteen and medium to large meeting room operating
capacities are set to 50%, labs are fully open, and the rest of the facilities remain closed). Figure
9a depicts active ofice-induced employee infections, Figure 9b shows cumulative infections.
While there is a possibility of significant rise in ofice induced infections with 50% occupancy,
this sudden rise is rather miniscule in absolute numbers.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusion</title>
      <p>As decision-makers devise post-pandemic workplace strategies, it is critical to appropriately
model the influencing dimensions of the enterprise ecosystem for evaluating the impact of the
candidate strategies on employee infections and project timelines. Complexities arise from
the varying nature of the sub-systems in terms of scale, characteristics, level of granularity,
uncertainties, and data availability. Given the multi-granular nature of the system, traditional,
single-methodology simulation approaches pose significant challenges necessitating the use
of integrated modelling approaches to overcome the limitations of the individual modelling
paradigms. We presented one such approach that combines SD and ABM, explained the rationale
of the modelling choices, illustrated the model building process, and presented a sequential
approach of model integration. The discussed approach modelled the aggregated structures
from a societal perspective and finely detailed structure of characteristics and behavior as
hierarchical decomposition structures from enterprise perspective. This approach overcomes
the issues of data availability and scale while still allowing for a more explicit representation of
the system and supports strategy evaluation to enable decision making under uncertainty within
continually changing pandemic landscape. Our future work includes modelling and simulating
complex domains like sustainability, incorporating other classes of SD-ABM integration, and
integrating other kinds of modelling techniques.
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