# CITY-SCALE SIMULATION OF COVID-19 PANDEMIC & INTERVENTION POLICIES USING
AGENT-BASED MODELLING

Gaurav Suryawanshi
Department of Mathematics
Indian Institute of Technology Kharagpur
Kharagpur, INDIA, 721302
Varun Madhavan
Department of Chemical Engineering
Indian Institute of Technology Kharagpur
Kharagpur, INDIA, 721302
Adway Mitra
Centre of Excellence in Artificial Intelligence
Indian Institute of Technology Kharagpur
Kharagpur, INDIA, 721302
Partha Pratim Chakrabarti
Centre of Excellence in Artificial Intelligence,
Department of Computer Science and Engineering
Indian Institute of Technology Kharagpur
Kharagpur, INDIA, 721302

## ABSTRACT

During the Covid-19 pandemic, most governments across the world imposed
policies like lock-down of public spaces and restrictions on people’s
movements to minimize the spread of the virus through physical contact.
However, such policies have grave social and economic costs, and so it is
important to pre-assess their impacts. In this work we aim to visualize the
dynamics of the pandemic in a city under different intervention policies, by
simulating the behavior of the residents. We develop a very detailed agent-
based model for a city, including its residents, physical and social spaces
like homes, marketplaces, workplaces, schools/colleges etc. We parameterize
our model for Kolkata city in India using ward-level demographic and civic
data. We demonstrate that under appropriate choice of parameters, our model is
able to reproduce the observed dynamics of the Covid-19 pandemic in Kolkata,
and also indicate the counter-factual outcomes of alternative intervention
policies.

##  1 INTRODUCTION

The Covid-19 pandemic, caused by the SARS-COV-2 virus, broke out from Wuhan in
China in December 2019, and has spread to almost every country of the world.
Till March 2021, nearly 120 million people have been affected so far, with
over 2 million deaths. Among the countries most severely impacted in terms of
total caseload and total number of deaths is India, which has a vast
population of nearly 1.4 billion and moderately high population density of 382
persons per Sq Km. The large and populous cities of India have faced high
caseload. One of the largest and most densely populated cities in India is
Kolkata, located in the eastern part, which has had its share of cases in the
pandemic.

In the absence of medicines or vaccines specifically equipped to tackle this
disease, most national, regional and local governments across the world have
resorted to non-pharmaceutical interventions (NPI), such as prescription of
face-masks and hand sanitizers, and maintenance of “physical distancing”
through stay-at-home orders, partial or total closure of public spaces like
schools and offices, and so on. While such measures may be useful in slowing
down the pandemic spread, they cannot be sustained long due to their
disruptive effects on society and economy. This disruption is particularly
severe in places like India where a large part of the population earn their
livelihood through daily wages. Governments have to make a trade-off between
public health and economics while implementing policies on NPIs. This
necessitates the assessment of policy impacts, which may be achieved through
computer simulations of the societal impacts of the pandemic as well as
various intervention policies.

Traditionally, pandemics have been simulated using epidemiological models.
However, such models usually operate at very course scales by considering
gross statistics such as number of infected people, and cannot take into
account spatial aspects of the pandemic spreading process. To simulate the
pandemic spreading process under real or hypothetical policy interventions, it
is necessary to understand the daily lifestyles and social contacts of
individuals and the associated spatial structures. It is here that agent-based
models become important, as they can provide a representation of individual
behavior at high spatial and temporal resolution. The models can take into
account both spatial and social structures in a limited region, such as a
city. An agent-based model can be used to emulate the daily activities of
individuals under the influence of the pandemic and the NPIs, and observe the
resultant impacts. Once the model is validated against actual observations, it
can be used to simulate counterfactual or “what-if” scenarios, such as
alternative NPI policies, and assess their impacts. During the Covid-19
pandemic, several research groups all over the world have been developing
agent-based models for specific cities, or larger regions [29]. Different
models have different levels of detailing with respect to the region of study,
and may include any subset of features such as demographic factors, family
structures, spatial layout, residential areas and public spaces, transport
systems, daily schedule of people and so on.

This paper presents another agent-based model for simulating the pandemic in
cities. To the best of our knowledge, our model has the highest level of
detailing, and we explicitly emulate all the features mentioned above. We also
have additional features such as compliance rates, i.e. the probability that
any individual will obey the operational NPI. In this study, we have collected
the parameters specifically for the city of Kolkata, and validated the model
by reproducing the time-series of daily infections of Covid-19 as observed in
the records. We have demonstrated that explicitly emulating the aforementioned
city structures in the model improves this validation. Additionally, we have
also analyzed a number of “what-if” scenarios about alternative NPI policies
such as no lockdown, localized lockdowns in hotspots, and partial closing of
workplaces.

##  2 RELATED WORK

In this section, we review the relevant literature on agent-based models and
their applications to modeling cities and pandemic spreading.

Agent-based Simulation: Agent-based modeling (ABM), as a computational
technique, emerged in the 1990s, primarily in the domain of computational
social science [8, 4] as a testbed for artificial societies. It was also used
in the domains of economics [26], ecology [10] and population biology [5]. Its
potential for modeling urban systems was noted by [22] to capture various
stakeholders, urban components and their interactions, such as the work by
[2], [3] that explored the temporal changes in urban sprawl and land-use using
cellular automata-based and agent-based models comparatively. Agents were used
to represent individual residents in cities and rule-based modeling of their
interactions was developed [13, 21]. More recent urban ABMs focus on specific
aspects of cities in greater details, such as residential areas [23], and
transport [17, 12, 18]. MATSIM [16] and UrbanSim [30] are ABM-based software
packages to simulate long-term trends in a city related to traffic management,
electricity/water usage and gas emissions etc, for use in multi-dimensional
policy planning. [9] focus on the intersection between urban mobility,
equitable accessibility and air pollution using ABMs.

Epidemic Model: Epidemiology, or the dynamics of epidemics have traditionally
been studied with differential equation-based compartmental models such as
Susceptible-Infected-Recovered (SIR). However, such models deal with only
gross statistics of pandemic such as number of susceptible or infected people,
without a realistic representation of how infections may spread from person to
person depending on their locations and interactions. So modern epidemiology
is turning towards ABMs, such as [24, 1, 28, 6]. Such models need i) a
synthetic population with realistic demographic attributes, ii) a geo-located
social network of the population, and iii) a disease progression and infection
model. The spread of any epidemic in an urban area is strongly dependent on
the transportation systems, and this is captured in the recent study by [11]
using agent-based models and MATSIM software for transport systems. Other
examples of agent-based models using networks are [7, 20].

During the Covid-19 pandemic, agent-based models have acquired special
attention worldwide, as policymakers are interested to assess the impacts of
various non-pharmaceutical interventions (NPI). Such impacts may be desirable
(slowing down of pandemic spread) or undesirable (economic disruption). The
study [25] proposes COVID-ABS model to study the impact of various NPIs on
both public health and economics by emulating a closed society including its
people and decision-makers. This framework uses SEIR-type disease model and
considers demographic and economic attributes and daily schedules of people.
The parameters of this model have been chosen based on Brazil, but can also be
used for any other place. A similar study [15] was done for France, using
detailed attributes related to demographics and social contact structure of
the agent population, and a small statistical model for city spaces and
transport. Another similar model was built for cities and validated on Ford
County, Kansas, USA using mostly demographic attributes of the agents, along
with smartphone-based contact tracing. Another study [27] was built
specifically for small cities, taking into account the basic structure of the
city, population demographics, testing and contact tracing, and calibrated
with New Rochelle, New York. This model also includes confounding due to
covid-like symptoms and vaccination, along with a detailed scenario analysis.
Several other studies like [19, 14] also present similar models validated on
particular cities or regions.

Based on the above survey, we identify several features related to modeling
Covid-19 pandemic in cities. Each of the studies takes into account a subset
of these features. In Table 1, we list out these features, showing which study
takes into account each feature elaborately with high (H), medium (M) or low
(L) model complexity. High model complexity means that there are separate
variables with attached stochastic processes representing the feature, medium
complexity means that it is managed with proxy parameterization, and low
complexity means that the feature is not represented at all. These features
include the disease model, demographic attributes and their daily schedule
related to agents, the spatial layout of the city with locations of
residences, workplaces etc, the transport system and medical facilities of the
city. Other features include economic impacts, vaccination, and the presence
of confounding diseases with similar symptoms. Other important features of
these models are their analysis of various hypothetical scenarios related to
intervention policies, and validation of the models by demonstrating their
ability to reproduce the actual observations related to number of daily cases,
deaths etc in the target location.

Table 1: Comparison of different agent-based models for Covid-related scenario analysis, in terms of urban features (H-High, M-Medium, L-Low) considered by them Features | Silva et al | Hoertel et al | Truszkowska | Shamil et al | Kerr et al | This Work
---|---|---|---|---|---|---
|  |  | et al |  |  |
Disease Model | H | H | H | H | H | H
Demographic attributes | H | H | H | H | H | H
Daily Schedule | H | M | L | L | L | H
City Structure | L | M | H | L | L | H
Workplaces | M | M | H | L | M | H
Transport Systems | L | M | L | L | L | M
Medical Facilities | L | L | M | L | L | M
Contact Tracing | L | L | H | M | M | H
Economic Impacts | H | L | L | L | L | L
Confounding | L | L | H | L | L | L
Vaccination | L | L | H | L | L | L
Scenario analysis | H | H | H | H | H | H
Validation | M | H | H | H | H | H

##  3 MODEL COMPONENTS

###  3.1 Agents

The agents of this model are the individuals, i.e. the residents of the city.
Each agent is associated with attributes shown in Table 3.

###  3.2 City Model

A city contains many kinds of spaces - residential, workplaces, marketplaces
etc, as well as different kinds of facilities and services. In this work, we
consider statistical models for the following.

Centres of Economic activity or Workplaces: The economic activities of the
city are driven by several industries. The economic sphere is divided into
sectors, which are further divided into sub-sectors. Each sub-sector then
contains a number of workplaces under it. Workplaces are locations where
agents go for work. Each workplace is assigned with location co-ordinates.
Also, agents representing working individuals are associated with a workplace.
Each workplace holds two kinds of people, one is one-time visitor and others
are daily wage workers. A workplace has attributes as shown in Table 3.
Further, the workplaces in different sectors (education, healthcare, hotels
etc) have different characteristics related to the exposure and physical
interactions among the workers, which has a bearing on the infection spread.
These characteristics are detailed in Table 5, with reference to Kolkata city.

Transportation: There are two kind of transportation, inter-city and intra-
city. Intra-city transport enables citizens to travel from one place to
another within the city, especially home to workplace. Although such transport
can be either public or private, we ignore private transportation in this
model since disease infection in a private vehicle is highly unlikely.

Healthcare: The crucial healthcare sector consists of a network of COVID-19
Hospitals, COVID-19 Healthcare centres, COVID Isolation Centres. Each of these
facilities are associated with a location, and has a fixed capacity. The
attributes of healthcare facilities are mentioned in Table 3.

Education: In this model, education has been treated separately from the
economic sectors, due to the extremely high number of students. These students
may be interpreted as an employed workforce generating negligible economic
output. Colleges and places of higher education are also under the Education
sector. Each educational institute too is associated with a location and
capacity. Each agent representing an individual who is a student is assigned
to an educational institute (school or college), depending on age.

Table 2: Agent attributes. Property |  Basis |  Description
---|---|---
ID |  $Z$ |  ID of the person
Age |  $Z$ |  Age of the person
Age Group |  $Z$ |  Bands of 10 years
Family ID |  $Z$ |  Assigned to a family
isCitizen |  {0, 1} |  resident of the city or not
Workplace |  $Z^{3}$ |  3-D vector (Sector, Sub-Sector, Workplace ID)
Visiting Places |  $Z^{n}$ |  $n$-D vector - frequently visited places
Comorbidity |  {0, 1} |  has co-morbidity or not
Income level |  $R$ |  Family daily income
Occupancy |  $Z$ |

Table 3: Workplace attributes. Property |  Basis |  Description
---|---|---
ID |  $Z$ |  Id of the workplace
Sector |  $Z$ |  Economic Sector to which workplace belongs
Sub-Sector |  $Z$ |  Sub-sectors within sector
Location |  $R^{2}$ |  (Latitude, longitude) of the workplace
isEssential |  {0, 1} |  whether the workplace is essential
Workers |  $Z^{n}$ |  $n$-D vector, list of people working
Visitors |  $Z^{n}$ |  $n$-D vector, list of people visiting
Income level |  $R$ |  Daily economic output of the Workplace

###  3.3 Infectious Model

Now we come to the most crucial part- the Covid-19 infection model. For this
model, we define the following _states_ , such that each agent is associated
with one state at every time-step.

Each agent consists of a state belonging to a finite state machine, which is a
vector of dimension 2. First dimension represents the virus-related state i.e
Healthy (H), Infected (IF) and Recovered (R) and Dead (D). Infected state has
two sub-parts namely Symptomatic (S) and Asymptomatic (A). We call them Virus-
State ($S_{v}$). Second dimension represents mobility-related state which are
Free (F), Out-of-City (O), Quarantined (Q), Isolated (I) and Hospitalized
(HP). We call them Mobility-State ($S_{m}$) These two kinds of states are
independent of each other, and the final state consists of a concatenated
vector of these two.

Regarding the Virus-state, initially every person is assumed to be healthy
(H). When a person in state $H$ comes in contact with a person in state $IF$,
the former gets infected with a certain probability. The viral load (VL) of a
newly infected person is assumed to follow a Beta distribution, scaled
appropriately. If this load is below a threshold, the person remain
asymptomatic. Otherwise, the person undergoes a fixed incubation period after
infection, after which they start showing symptoms. The peak infection period
is sampled from a Gaussian distribution, after which the person may die or
start recovering (depending on age and co-morbidity). The time taken to
recover is also considered to follow a Gaussian distribution.

Infection can spread from one person to another with a certain probability
whenever they share the same physical space. This probability is a function of
the contact duration and physical distance between them. This is why we have
considered number of work-hours and physical gap as attributes of workplaces.

###  3.4 Simulation Methodology

Having described the model in details, we now come to the simulation part. The
simulation proceeds by initializing the system, which includes setting up all
the agents and their attributes, workplaces, medical facilities etc. This is
done by sampling from probability distributions, such that all the attributes
are consistent with each other. We then set the hyper-parameters of the model
such as parameters of various distributions in section 3.3. Additionally we
define Compliance Rate: the proportion of population actually following the
policy in place. Higher compliance rates means no two agents meet beyond their
daily schedule. A small random subset of the population is infected with the
disease as initialization. After that, we begin the simulation for the
specified period. At each time-step we sample the movements of each agent
according to a stochastic process based on their daily routine, whose
distributions are based on the agent’s workplace, residence and travel
preferences. We track the interactions between pairs of individuals (when they
come spatially close during their movements), and in such cases infection may
take place stochastically as explained above.

Table 4: Healthcare workplace attributes. Property |  Basis |  Description
---|---|---
ID |  $\mathcal{Z}$ |  Id of the workplace
Number of beds |  $\mathcal{Z}$ |  Number of beds that the place is able to host
Workers |  $\mathcal{Z^{n}}$ |  Workers working at the hospital
ICU beds |  $\mathcal{Z}$ |  Numbers if beds at the intensive care facility
Ventilators |  $\mathcal{Z}$ |  Crucial resource whose availability can affect death rates
Type |  {Free, Paid} |  Whether the hospital is free for everyone or one has to pay

Table 5: Workers per sector. Sector |  No. of worker |  No. of centers |  working hours |  Physical gap
---|---|---|---|---
Education |  720801 |  13900 |  8 |  0.5
Commerce |  45329 |  120 |  8 |  3
Healthcare |  22634 |  [16, 22, 19] |  0 |  2
Agriculture |  1512 |  170 |  8 |  5
Manufacturing |  136549 |  450 |  8 |  2
Mining |  20 |  3 |  8 |  1
Utilities |  22202 |  55 |  8 |  2
Construction |  444782 |  1472 |  8 |  5
Hotel |  962881 |  4162 |  8 |  2
Finance |  626412 |  2068 |  8 |  3
Social |  341858 |  1792 |  12 |  1

##  4 RESULTS FOR KOLKATA CITY

We parameterized the above simulation framework according to Kolkata, a city
in Eastern India, as a test case. We initialized it by injecting actual data
related to this city as the model’s parameters and attributes.

###  4.1 City-scale Data for Kolkata

To set the attributes and parameters for the simulation in Kolkata, we
utilized the following sources of information:

Demographics: Distribution of population across the wards of the city,
including the number of people in each ward and the population density of each
ward are available at:
https://censusindia.gov.in/pca/pcadata/pca.html,https://censusindia.gov.in/2011census/population_enumeration.html

Medical facilities: Distribution of Covid Quarantine Centres, Covid Care
Centres and Covid Hospitals across the wards are available at
https://www.wbhealth.gov.in/uploaded_files/corona/Notification___Revised___67_Covid_Hospital___30.04_.2020_.pdf,
https://www.wbhealth.gov.in/uploaded_files/corona/Covid-19_Pvt_Hospitals_Kol_Isolation_22_March_20.pdf

Covid testing facilities: The Covid-19 testing capacity in Kolkata are
available at
https://www.wbhealth.gov.in/uploaded_files/corona/Order_157_05052020_For_attention_of_the_Public_SB_Secy.pdf

Educational centres Distribution of schools and colleges across the wards are
available at
http://www.wbpublibnet.gov.in/sites/default/files/sites/default/files/sites/default/files/uploads/pdf/school_list_kolkata.pdf,
https://wbhed.gov.in/page/govt_colleges.php

Figure 1: Population density in Kolkata city

Figure 2: Baseline positive cases per million

###  4.2 Model Simulations

The simulation was started from May 3rd, 2020. This is the date from which we
have the Kolkata district level data. Although entire India went into lockdown
since 25th March 2020, all COVID-19 related data was published state-wise till
3rd May. Since there is a gap between data availability and start of pandemic,
we need to specify the number of infected people till this date. For this
purpose, we used reverse simulation, i.e. start the simulation from March 25
with various random initializations and identify the one for which the
”Positive Tested” count on May 3 matches the recorded data (651) for the same
day. The number of active cases (1495) on that day was then obtained from that
simulation.

The lockdown policy, containment zone policy, testing capacity and public
transport capacity were set precisely as actually followed in the city of
Kolkata. We used publicly available data Covid-19 India API for the same. The
education sector (schools and colleges) in Kolkata can be a major source of
infections due to high density of students/teachers. Hence the state
government kept all schools and colleges shut through the year. The same is
assumed in the simulations.

To fit the predicted cases to the actual number of cases, we used grid search
on parameters such as Compliance Rate and IFP values during each month, upto
the month of October. The compliance rate with the policies mentioned above
were chosen to be 0.5 during May 1 - May 14, 0.8 during May 15 - July 31, and
0.4 from August 1 onwards. This was done to mimic tendency of poeple to follow
the rules. The effect of varying these values are discussed in Section 5. The
probability of infections (IFP) via external transportation routes was chosen
to be 0.01 in June (as most transport services were closed), which was
increased gradually to 0.25 in September. Contact Tracing efficacy was chosen
to be 60% for workplace contacts and 30% for transport contacts.

The simulation was carried out with the above model, along with the parameter
settings mentioned above for the period May 3 to 1 October. For each parameter
setting, the simulation was run 10 times, and the mean values reported. The
number of new daily infections as obtained by the model are plotted in Fig
4(ward distributed) against the number of new daily infections as reported
here. In 108 out of 152 days, simulation error remains within the 10% . Most
of the errors related to prediction occur during the early parts of the
simulation which is expected, as the pandemic had started well before the
simulation start date as mentioned in section 4.2. In Figures 1-3 we can see
the 141 wards of the city, and the simulated number positive cases per ward.
We see a strong correlation between the densities of Ward and cases,
indicating a confirmation on trends we have seen globally.

###  4.3 Simulations with Simplified Model

As a possible alternative to using this fine-grained ward-level data, we
attempted to recreate the simulation with a simplified version of the model
which assumes uniform distribution of all parameters, i.e. population,
population density, density of hospitals etc, across all wards leaving rest of
the hyper-parameters as same. We observe in Figure 4 that this simulation does
not perform as well as our proposed model’s simulation, as the daily error is
higher on most days. This suggests that high spatial granularity is important
for successful simulation of pandemic in cities.

Figure 3: Comparison with reduced model, here Actual represents the Ground
truth, Kolkata Ward Distributed represents the simulation with true ward
population distributions and Equal Distribution represents the simulation with
equally distributed ward population.

##  5 ”WHAT-IF” ANALYSIS OF COUNTERFACTUAL SCENARIOS

The real aim of this kind of simulation is to generate and analyze
counterfactual scenarios, such as what could have been possible results of
alternative policies had they been implemented. Using our agent-based
simulator, we predict the outcome of various scenarios (i.e. intervention
policies) by adjusting the parameters accordingly.

  * •

Lockdown Phases: We consider the following lockdown parameters -

    * –

Start date of lockdown \- date when the lockdown comes into effect

    * –

Duration of lockdown \- the number of days for which the lockdown is in effect

    * –

Type of lockdown \- the lockdown can be either city-wide, or limited to
specific wards or zones with high number of cases.

  * •

Use of Public Transport: This is the fraction of the total population who are
expected to use public transport on daily basis. In Kolkata city, this ratio
is estimated to be about 0.17.

  * •

Extent of Physical Distancing: Transmission probability between two persons
depends on the distance between them.

  * •

Contact tracing efficacy: whenever any person tests as positive, what fraction
of their close contacts are identified for testing?

  * •

Compliance Rates: the effect of choosing a range of Compliance Rates

###  5.1 Scenarios Evaluated

Figure 4: Long lockdown.

Figure 5: No Lockdown + Only Education Sector Locked + Multiple Short
Lockdowns.

Figure 6: Effect of reduced public transport usage.

Figure 7: Contact Tracing Efficacy.

Figure 8: Effect of compliance rate.

Figure 9: Effect of social distancing.

  * •

Lockdown Variations

    * –

Long lockdown: Lockdowns of 30, 45, 60, 75 and 90 days were simulated from May
1st. This scenario was tested to see whether the virus could be completely
exterminated with a long lockdown. Out-of- city travel was completely stopped
and the Education sector was kept locked throughout the simulation. The
results are shown in Figure 5. We find that prolonging the lockdown does not
help as cases shoot up later.

    * –

Multiple short lockdowns: We wanted to evaluate the effect of shorter
lockdowns at regular intervals instead of one long lockdown. Hence, the entire
city (all sectors across all wards) were locked down on either i) The last two
days of each week, or ii) The last one week of each month. The results are
shown in Figure 5, and we find that weekend lockdown does work quite well. We
also consider the possible effects of closing down only the education sector,
and not locking down at all. It is found that the last scenario would have
resulted in more than 10 times increase in the number of cases.

  * •

Effect of reduced public transport usage: This fraction was estimated to be
about 0.17 in Kolkata prior to the pandemic. Hence, to account for lesser
number of people opting for public transport, we see the effect of setting
this fraction to [0.01, 0.05, 0.085, 0.1]. The results are shown in Figure 7

  * •

Contact tracing efficacy: To study the impact of changes in the efficacy of
Contact Tracing, we varied the accuracy as follows: i) Workplace contact
tracing efficacy - [60%, 70%, 80%, 90%, 100%], and ii) Transport contact
tracing efficacy - [30%, 40%, 50%, 60%, 70%, 100%] - indicating that those
fractions of the contacts of each new positive case are traced. The results
are shown in Figure 7.

  * •

Effect of compliance rate: To evaluate the impact of having uniform compliance
rates, we kept the Compliance Rate constant throughout the simulation, at
[0.8, 0.7, 0.6, 0.5, 0.4, 0.3]. The results are shown in Figure 9

  * •

Effect of physical distancing: We evaluated the effect of having different
physical distancing factor (inter-person distance in the calculation of
transmission probability). The inter-person distance was multiplied by a
constant factor $SD_{factor}$ across all sectors. We evaluated the effect of
setting $SD_{factor}$ as [2, 1.8, 1.6, 1.4, 1.2, 1, 0.8, 0.6, 0.4]. The
results are shown in Figure 9

In general, the results indicate clearly that the total number of cases can be
controlled by high contact tracing, compliance rate and physical distancing.
Prolonged lockdowns are unlikely to help, though lockdown on every weekend
seems to be quite effective.

##  6 CONCLUDING DISCUSSION

In this paper, we discussed an agent-based model for simulation of Covid-19
pandemic in a city, that helps in assessment of intervention policies. The
uniqueness of this model lies in the highly granular representation of the
city including ward-level demographics, workplaces and healthcare facilities,
as well as public transport usage and compliance rates etc. We also show that
such granular representations are necessary for successful simulation. This
model can work as a digital twin of a city, irrespective of the pandemic.
Future improvements to this model will be to include vaccinations and economic
impacts of the pandemic and policies. Another future goal is to use machine
learning to estimate the parameters of the model. The most important usage of
these models is their usage in ”what-if” analysis. In this case, we explored
the space of possible outcomes of different policies, and predicted possible
results. Although it is impossible to confirm the accuracy of these results as
they counterfactual, clearly they are consistent with common sense. A future
direction of work will be to cast these in the framework of reinforcement
learning and adaptively search the sequence of optimal policies.

## ACKNOWLEDGMENTS

This work was partially funded by Google Tensorflow Research Award, 2019 to
IIT Kharagpur, and by the Department of Science and Technology, Government of
India under its RAKSHAK scheme. We acknowledge the contributions of several
students such as Shubham Mishra, Sparsh Kumar Jha, Sakshi Dwivedi and faculty
members such as Profs. Sudeshna Sarkar, Debdoot Sheet and Arijit Mondal, all
from IIT Kharagpur. We especially thank Prof. Bharath Aithal for providing us
with the ward-wise datasets of Kolkata.

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