ifaamas [AAMAS ’24]Proc. of the 23rd International Conference on Autonomous
Agents and Multiagent Systems (AAMAS 2024)May 6 – 10, 2024 Auckland, New
ZealandN. Alechina, V. Dignum, M. Dastani, J.S. Sichman (eds.) 2024 2024 537
Massachusetts Institute of Technology Cambridge, Massachusetts United States
University of California San Diego San Diego, California United States
Massachusetts Institute of Technology Cambridge, Massachusetts United States
Massachusetts Institute of Technology Cambridge, Massachusetts United States

# First 100 days of pandemic; an interplay of pharmaceutical, behavioural and
digital interventions - A study using agent based modeling

Gauri Gupta<EMAIL_ADDRESS>,  Ritvik Kapila<EMAIL_ADDRESS>,  Ayush Chopra
<EMAIL_ADDRESS>and  Ramesh Raskar<EMAIL_ADDRESS>
###### Abstract.

**footnotetext: Equal contribution

Pandemics, notably the recent COVID-19 outbreak, have impacted both public
health and the global economy. A profound understanding of disease progression
and efficient response strategies is thus needed to prepare for potential
future outbreaks. In this paper, we emphasize the potential of Agent-Based
Models (ABM) in capturing complex infection dynamics and understanding the
impact of interventions. We simulate realistic pharmaceutical, behavioral, and
digital interventions that mirror challenges in real-world policy adoption and
suggest a holistic combination of these interventions for pandemic response.
Using these simulations, we study the trends of emergent behavior on a large-
scale population based on real-world socio-demographic and geo-census data
from Kings County in Washington. Our analysis reveals the pivotal role of the
initial 100 days in dictating a pandemic’s course, emphasizing the importance
of quick decision-making and efficient policy development. Further, we
highlight that investing in behavioral and digital interventions can reduce
the burden on pharmaceutical interventions by reducing the total number of
infections and hospitalizations, and by delaying the pandemic’s peak. We also
infer that allocating the same amount of dollars towards extensive testing
with contact tracing and self-quarantine offers greater cost efficiency
compared to spending the entire budget on vaccinations.

###### Key words and phrases:

Agent-based Models; Computational Epidemiology; Sensitivity Analysis; Contact
Tracing Intervention; COVID-19 Pandemic

##  1\. Introduction

The recent outbreaks of COVID-19 have left an indelible mark on society at a
global scale, highlighting the vulnerability of public health Miyah et al.
(2022); Lewis et al. (2022). Thus, deepening our insights into how pandemics
evolve is imperative, ensuring that our actions are prompt, effective, and
grounded in evidence Amzat et al. (2020); Tam et al. (2020). Given the
unprecedented nature of these pandemics, it is inherently challenging to
simulate their dynamics. Agent-based modeling has emerged as a pivotal tool
for replicating the complex dynamics inherent in the pandemic evolution
Romero-Brufau et al. (2021); Abueg et al. (2021); Aleta et al. (2020); Kerr et
al. (2021). Agent-based models (ABMs) are distinct in their ability to provide
a granular view of disease propagation by analyzing both micro-level
interactions and the broader emergent phenomena, making them particularly
suited for delineating the effects of potential interventions.

In the past, governments globally adopted varied strategies to counteract the
spread of infections, particularly during COVID-19 Haug et al. (2020); Brauner
et al. (2021). Some of these were effective, while some were not Flaxman et
al. (2020); Banholzer et al. (2021). Interventions such as delayed travel bans
proved insufficient, allowing for rapid global infection spread Tellis et al.
(2020), while prolonged severe lockdowns crippled global economies Yanovskiy
and Socol (2022). Additionally, the deployment of digital initiatives for
contact tracing Cheng et al. (2020); Raymenants et al. (2022); Willem et al.
(2021); Barrat et al. (2021) had a limited impact due to low adoption and
delays in user quarantine post-exposure Davis et al. (2021). As notified users
awaited test results, potential carriers inadvertently continued activities,
making this approach largely ineffective in curbing transmission Li and Guo
(2020); Chowdhury et al. (2020). Pharmaceutical interventions, once viewed as
the primary defense against the pandemic, encountered their own set of
challenges Xiao et al. (2020). The apprehension over the longevity of vaccine-
induced immunity and potential side effects further hampered the pace of
vaccination drives Subbarao (2021); Odone et al. (2020). Moreover, by the time
effective vaccines were produced, many nations had already peaked in
infections Pandey et al. (2021). Thus, reflecting on these previous strategies
to understand what worked and what did not is crucial for developing efficient
future pandemic responses.

However, decision-making in such scenarios is challenging due to the
multifarious intricacies of complex societies characterized by heterogeneous
populations, diverse behavioral patterns, and differential access to resources
Alsalem et al. (2022); Angeli and Montefusco (2020); Chang et al. (2021). The
interplay of various interventions, their mutual impacts, and the factors
influencing their effectiveness adds further layers of complexity. In this
paper, we address these challenges of modeling real-world simulations in
complex societies by considering varied populations with interaction networks
spanning across household, occupational, and random graphs. We consider
behavioral patterns through app adoption rates, self-quarantine, and
compliance probabilities. Further, we model differential access to resources
stratified by age or policy choices, for instance, prioritizing higher age
group individuals for vaccination and age-based app adoption.

We model the progression of a pandemic over its initial 6 months (180 days)
using real-world socio-demographic (census) data from Kings County,
Washington, evaluated at scale of 100,000 agents. For our analysis, we
simulate three main types of interventions: pharmaceutical, behavioral, and
digital, and highlight the effectiveness and potential pitfalls of each
approach in controlling future pandemics. We not only assess these individual
interventions but also integrate a collective interplay of these
interventions, suggesting they are complementary to each other, not alternate.
Pharmaceutical interventions include vaccination drives and testing to detect
cases. Behavioral interventions include self-quarantine upon testing positive
and individual responsiveness and adherence to recommended actions. The
lockdowns many countries implemented can be viewed as a prolonged strict self-
quarantine. Digital interventions explore tools such as contact tracing apps
designed to monitor and curtail spread through tracking interactions. Our
extensive analysis suggests relying solely on rapid vaccine development for
outbreak control isn’t viable. Enhanced preparedness demands an integration of
pharmaceutical approaches with contact tracing and behavioral strategies,
ensuring a holistic, prompt response.

The following are the major contributions of our paper: (1) We introduce a
general pipeline using ABMs that simulates a real-world synergy of
interventions at scale, encompassing pharmaceutical, behavioral, and digital
strategies. This framework offers extensive detail to capture the complexities
observed in the real-world adoption of these interventions. (2) Our user-
friendly and flexible framework is designed with a customizable configuration
file enabling non-technical people like epidemiologists and policy-makers to
study the effect of intricate interventions on pandemics. (3) We provide a
comprehensive cost analysis of pandemic containment under each intervention
strategy. (4) We perform extensive experiments on real-world data from Kings
County, Washington for COVID-19. Our findings deepen the understanding of
pandemic trends and offer valuable policy recommendations for effective
pandemic response. (5) Some of our interesting insights are: (a) The first 100
days of the pandemic are a pivotal threshold in determining the course of a
pandemic’s trajectory. (b) Pairing delayed vaccination with digital and
behavioral interventions proves more impactful than solely pushing for early
vaccination, as it not only reduces overall infections and hospitalizations
but also delays their peak. (c) With a fixed $0.5M budget, investing in
testing with self-quarantine and digital contact tracing is more effective
than funding early vaccinations alone.

##  2\. Related Work

Agent-based models (ABMs) are discrete simulators that allow entities (agents)
with designated characteristics to interact within a given computational
environment, replicating complex systems Bonabeau (2002); Norton et al.
(2019); Reiker et al. (2021); Zheng et al. (2022); Dimitrov and Meyers (2010);
Hethcote (2000). Recently, ABMs have been widely employed in epidemiology to
understand disease progression and the efficacy of interventions by providing
relevant information to investigate and predict the behavior of the pandemic
Marathe and Vullikanti (2013); Romero-Brufau et al. (2021); Abueg et al.
(2021); Aleta et al. (2020); Kerr et al. (2021). Several studies have utilized
ABMs to evaluate the effectiveness of different interventions, such as social
distancing, quarantine, lockdown, and vaccination Hinch et al. (2021); Chopra
et al. (2021); Romero-Brufau et al. (2021). ABMs have also been used in prior
works for addressing policy-related queries like evaluating the importance of
test turnaround time versus its sensitivity Larremore et al. (2021), and the
benefits of postponing the vaccine’s second dose to focus on the distribution
of the first dose Romero-Brufau et al. (2021).

However, the utility of ABMs for practical decision-making depends upon
several factors. These include their accuracy in replicating the population
behavior Pellis et al. (2015); Groff et al. (2019). Furthermore, ABMs are
conventionally slow. A single forward simulation over a large ABM can take
several days Aylett-Bullock et al. (2021); Bisset et al. (2009). ABM
simulations are difficult to scale to large populations Bisset et al. (2009),
and are tough to calibrate with real-world data Pellis et al. (2015).
Moreover, they only simulate the effect of one intervention at a time, where
real-world deployment of intervention strategies are intricately linked to
each other and should be studied with a combined effect of each of these Kerr
et al. (2021); Chopra et al. (2021); Hinch et al. (2021).

Only after overcoming these challenges in ABMs can their insights truly guide
strategic pandemic interventions. Our model provides a comprehensive system
that simulates interventions with real-world challenges of deployment or
adoption, representing them through quantifiable parameters. We adopt a
vectorized approach Chopra et al. (2021) which enables a fast, parallelized
simulation, allowing analysis of emergent behavior on a large-scale population
for millions of agents in a few seconds. We not only assess the individual
interventions but also integrate a holistic interplay of these interventions.

##  3\. Method

Figure 1 shows the pipeline for different interventions along with the
progression of disease stages. We build on existing open-source agent-based
modeling frameworks Chopra et al. (2021); Hinch et al. (2021), optimizing
large-scale simulations through matrix computations, leading to enhanced
computational efficiency. Our model addresses the potential variances in the
adoption of interventions by employing a stochastic approach, sampling from
Gaussian distributions based on a certain compliance level to predict
outcomes. We model these interventions with an unprecedented level of detail
with aspects that have not been explored in such granular detail in prior
research. This comprehensive approach not only facilitates the examination of
the individual impact of each parameter, but also provides insights into the
synergistic effects of these interventions on the pandemic response.

In our model, individual agents (and their states) are modeled as tensors.
Agents navigate through eleven potential disease stages: susceptible,
asymptomatic, presymptomatic (mild or severe), symptomatic (mild or severe),
hospitalized, in intensive care, recovered, immunized, or deceased. Infections
can propagate during any interaction between susceptible and infected agents.
These interactions span three networks: household, occupation, and random
encounters, which are represented as sparse adjacency matrices. Each such
interaction is a stochastic process with a certain risk of disease
transmission. The foundational assumptions about disease progression,
transmission dynamics, and network interactions align with prior agent-based
models Chopra et al. (2021); Romero-Brufau et al. (2021). We will now delve
into an in-depth examination of each intervention, detailing various
parameters and compliance factors reflective of real-world scenarios.

Figure 1. Implementation of different interventions - Testing, Self-
quarantine, Vaccination, and Contact Tracing. (1) Infection spreads through
the interaction of infected with susceptible agents, and the states of the
agents are then updated based on disease progression. (2) Upon experiencing
symptoms, exposed agents get themselves tested (3a) If tested positive, agents
undergo self-quarantine with compliance. A quarantined agent then engages in
no further interactions until the quarantine period ends. The interaction
graph of quarantine agents is thus an isolated point (3b) Agents that have not
tested positive or are not quarantined get vaccinated. Vaccination reduces the
susceptibility of an agent to infection risk (3c) In case of contact tracing:
interactions of the positively tested agents (that own app in case of DCT)
from the previous interaction graphs of past days are tracked; (4c) exposure
notifications are sent to the possibly exposed tracked agents (that own the
app in case of DCT); (5c) notified agents then opt for self-quarantine. (Last)
After simulating for N days, the aggregate statistics of the agent states are
computed. Agent states here are: susceptible (S), exposed (E), infected (I),
recovered (R), mortal (M), and vaccinated (V)

###  3.1. Testing

Agents who are exposed to infection and develop symptoms undergo testing.
Every diagnostic test is defined by three primary parameters: specificity,
turnaround time, and the duration of test validity. The turnaround time
accounts for any inherent delays in receiving test results, presented as a
dictionary detailing possible result dates and their associated probabilities.
The test validity indicates the duration for which the test results are
considered relevant. After this period, agents are expected to be retested.
Factoring in real-world delays related to the deployment of testing kits,
tests can be deployed in the model after some start date, marking the start of
distribution of that particular testing method to the public. Table 1 shows
the list of different parameters supporting the testing mechanism.

In our simulations, we employ two types of tests: (i) RT-PCR test, with a
specificity of 0.99 and a turnaround time of 1 to 3 steps (1 to 3 days)
uniformly distributed Chopra et al. (2021); Kostoulas et al. (2021), and (ii)
rapid point-of-care test, which offers slightly reduced specificity of 0.85
with a turnaround time of 0 steps (same day). To cater to varying diagnostic
requirements, these parameters can be adjusted, offering flexibility in
modeling different test types. By default, our model uses the more reliable
RT-PCR test for simulations unless specified otherwise.

Table 1. Description of Testing parameters Parameter |  Explanation
---|---
test_start_date |  Date on which testing begins
test_true_positive |  Prob. of a true positive result
test_false_positive |  Prob. of a false positive result
test_results_dates |  Potential dates of receiving test results
test_results_dates_probs |  Dictionary of probabilities associated with each test result date
test_validity_days |  Duration for test results validity
test_cost |  Average cost of production of a test

###  3.2. Self-quarantine(SQ)

Upon testing positive or receiving exposure notification, an agent undergoes a
14-day self-quarantine adhering to compliance. However, an agent might not
consistently adhere to the complete quarantine. To simulate such
imperfections, a daily dropout probability of 1% is incorporated to account
for potential non-compliance. During the quarantine period, the agent’s
interaction network effectively becomes isolated, leading to no interactions
with other agents. After successfully completing the quarantine period, the
agent’s capacity to transmit the infection is nullified, effectively resetting
their infectiousness to zero. Table 2 provides a detailed overview of
different parameters for modeling self-quarantine.

Table 2. Description of Self-quarantine parameters Parameter |  Explanation
---|---
quar_enter_prob |  Prob. with which an agent enters self-quarantine after testing positive
quar_break_prob |  Daily quarantine dropout probability due to non-compliance
quar_days |  Number of self-quarantine days

###  3.3. Vaccination(VACC)

We simulate a two-dose vaccination regimen with an extensive level of
granularity. A dose of the vaccine provides a certain probability of becoming
immune to infections, depending on whether it is a first or second dose.
Vaccines are administered in an age-prioritized fashion, with the oldest
individuals receiving their vaccines first, and first-dose candidates given
precedence over the second dose. We simulate a probabilistic immunity
conferred post-vaccination, where immunity is not immediate but materializes
after a stipulated delay post-inoculation. Table 3 illustrates the parameters
driving our vaccination models, such as the vaccine’s start date, daily
production rate, shelf life, and efficacy percentages for both doses.
Moreover, it also highlights potential dropouts - those who, after receiving
the first dose might choose not to return for the second, capturing a real-
world nuance in the vaccination process.

Based on Pfizer and Moderna’s trial data Self et al. (2021), we assume a 90%
efficacy for the first dose and a 95% efficacy for the second dose
administered 21 days later. All simulations, unless indicated otherwise,
presume vaccination commencement at t=10 with a daily vaccination rate of 0.3%
on a population of 100K based on U.S. vaccination rates and patterns observed
internationally Chopra et al. (2021).

Table 3. Description of Vaccine-related parameters Parameter |  Explanation
---|---
vacc_start_date |  Date on which vaccine drive begins
vacc_daily_prod |  No. of vaccine doses produced daily
vacc_shelf_life |  Duration before a vaccine dose expires
vacc_dose_delay |  Days after which the vaccine dose starts showing effect
vacc_dose1_priority |  Indicator if the first dose is prioritized over second in distribution
vacc_dose1_eff |  Efficacy of the first vaccine dose
vacc_dose2_gap |  Duration between the first and second doses of the vaccine
vacc_dose2_eff |  Efficacy of the second vaccine dose
vacc_dose2_drop |  Probability of an individual not returning for the second dose
vacc_price |  Cost for development of a single vaccine

###  3.4. Contact Tracing (CT)

We adopt a hybrid contact tracing approach where first exposure notifications
are dispatched to contacts of infected app users followed by manual follow-up
for non-compliant users and agents not owning the app. Below, we delve into
the specifics of digital and manual tracing methods.

Digital Contact Tracing (DCT): At the start of the simulations, agents own a
Digital Contact App (DCA) with a fixed adoption rate based on age-stratified
data. This app records interactions of an agent across all three networks:
household, occupation, and random, within a 7-day window. Note that
interactions are logged only if both agents have the app. When an agent with
an app tests positive, they can opt to notify exposed contacts via the DCA.
Recipients then undergo self-quarantine based on their compliance probability.
In our experiments, we simulate DCT assuming an average 40% app adoption rate
and 80% compliance rate for self-quarantine.

Manual Contact Tracing (MCT): Manual tracing is similar to its digital
counterpart, with a few key differences as illustrated in Figure 2. Unlike
DCT, MCT doesn’t require smartphone ownership and is unlikely to remember
random or casual encounters (like those in public transport or stores). Only
contacts within the household and occupational networks are traced through
MCT. Manual tracers interview an infected agent to identify and track the
potential contacts over the past N (=7) days. However, only a portion of the
true interactions are identified based on the likelihood of recalling them
(70%). From these, a subset responds based on a set probability. Successfully
contacted agents then self-quarantine with a compliance probability of 90%.

In a targeted two-step process of contact tracing, MCT and DCT leverage
coupled capabilities of human intervention with digital tools. Performing
manual contact tracing of targeted potential infected agents who either did
not own the app or ignored the digital notifications can significantly improve
the scale/outreach of the tracing efforts to contain the infection spread.
Table 4 details the parameters used to model contact tracing.

Table 4. Description of Contact Tracing parameters Parameter | Explanation
---|---
app_adoption_rate | Prob. of agents owning the app at the start of the simulation in DCT
max_contact_days | Number of days for which history of previous interactions are traced (unique for DCT and MCT)
test_inform_prob | Prob. to notify the contacts via DCA/MCT after testing positive (unique for DCT and MCT)
mct_recall_prob | Probab. that an individual recalls their contacts accurately during MCT
mct_reachable_prob | Probability that an individual is reachable for manual contact tracing
sq_comply_prob | Compliance prob. for quarantine upon succesful contact tracing (unique for DCT and MCT)
Figure 2. Comparison of Digital vs. Manual Contact Tracing: Digital tracing
requires app ownership for both interacting agents but can effectively track
unknown or random interactions, while manual tracing captures household and
occupational contacts but may miss random interactions

##  4\. Results

We study the impact of different interventions discussed above on disease
progression and pandemic evolution in a population with 100,000 agents over a
period of 180-time steps. In particular, we simulate Self-Quarantine (SQ),
Vaccination (VACC), and Contact Tracing (CT) interventions and evaluate their
outcomes. We ran experiments using real-world socio-demographic and geo-census
data from Kings County in Washington state. All the results correspond to the
mean and standard deviation aggregated over 10 independent runs of the
simulation.

We present our results in five sections. Section 4.1 examines the individual
effect of different interventions on the evolution of the pandemic outcomes.
Section 4.2 focuses on the age-stratified analysis for these individual
interventions. Section 4.3 delves into the overall cost analysis of individual
interventions, highlighting their financial implications. Section 4.4 provides
insights into the interplay of pharmaceutical, behavioral, and digital
interventions, allowing us to study their cumulative effect on the pandemic’s
trajectory. Section 4.5 shows the geographical progression of infections in
Kings County, WA, where we simulate a combination of all the interventions
together and compare the spread with the unmitigated no-intervention (NI)
case.

###  4.1. Analysis of individual impact of different interventions

Figure 3. Comparative analysis of the individual impact of different
interventions on pandemic progression; No Interventions (NI), Self-Quarantine
(SQ), Vaccination (VACC), and Contact Tracing (CT). (a) Peak hospitalizations
showcase the strain on healthcare under each scenario, with notable stress in
the NI and SQ cases. The dotted line represents the hospital bed availability
for Kings County, Washington (b) Daily new infection rates highlight the
efficacy of interventions, with CT significantly lowering the infection rate.
(c) Cumulative infections over time reveal the pervasive nature of the
pandemic in the absence of effective measures and a substantial reduction in
total infections under VACC, SQ, and CT.

To provide a baseline for the impact of the pandemic, we first investigate an
unmitigated scenario in which there are no interventions (NI). We compare this
baseline unmitigated scenario with interventions such as self-quarantine (SQ),
vaccination (VACC), and contact tracing (CT). Figure 3 details the comparative
analysis of the individual effect of each of these interventions in terms of
the number of severely affected individuals who require hospitalization, rate
of infection, and cumulative infections.

The uncontrolled pandemic (NI) peaks at t=65, with the number of
hospitalizations of 175, far exceeding the available capacity of 55 Liss and
Sumida ([n. d.]); cov ([n. d.]) by 218% as depicted in Figure 3(a). This
indicates the immense strain on the healthcare system in the no-intervention
case, pushing it to the brink of collapse. Figure 3(b) highlights a peak daily
infection rate of 281 per 100,000 agents in NI, with a staggering 81% of the
population infected by the end as visualized in 3(c).

In the SQ scenario, while the maximum rate of infections dropped by 45%
compared to the NI case, hospitalizations still peaked at 115, overshooting
the capacity by 109%. This suggests that self-quarantine alone without the
support of additional containment strategies is not a viable option. The VACC
strategy resulted in hospitalizations still peaking at 57% above the estimated
capacity, with daily infection rates nearing those in the NI scenario. For
both SQ and VACC strategies, around 70% of the population was infected by the
end of the pandemic. Interestingly, despite VACC’s high infection rate, we
observe fewer individuals needed hospitalization due to enhanced immunity
gained by the agents through vaccination.

In the case of contact tracing (CT), a huge reduction in hospitalizations from
the NI case is observed, bringing the peak very close (within 16%) to the
available capacity. Additionally, CT delayed the peak by 14 days, giving the
healthcare system more time to be prepared with the necessary resources. The
maximum rate of infections dropped by a massive 72%, with only 54% of the
total population infected by the end of the pandemic. Therefore, our
experiments indicate that CT with testing is the most effective standalone
intervention for pandemic containment.

Notably, irrespective of the specific intervention deployed, the peak
consistently occurs within the first 100 days for each individual strategy.

###  4.2. Age stratification of infections for different interventions

Figure 4. Age-stratified cumulative infections in Kings County, Washington,
illustrating the impact of contact tracing (CT), self-quarantine (SQ), and
vaccination (VACC) intervention scenarios on different age groups.

Figure 4 depicts the age-stratified cumulative infections in Kings County,
Washington. While implementing CT, we simulate the app distribution with an
average overall app adoption rate of 40% in an age-stratified manner, where
the age groups 20-59 have a higher probability of owning the app.
Consequently, we observed a large drop of 26% in cumulative infections for
agents in these age groups of 20-59. However, a significant drop
(approximately 40%) in cumulative infections in the age group 0-19, was also
observed even with relatively low app adoption rates. This is due to effective
manual contact tracing implementation within households.

For the VACC intervention case, we prioritize agents in higher age groups for
vaccinations. Hence, we observe a reduction of 82% and 92% infections for the
age groups 70-79 and 80-89, respectively, as compared to the NI case. These
drops are substantially high compared to the average drop in infections over
all age groups of 14%.

###  4.3. Cost analysis of individual interventions

Figure 5. Comparison of costs associated with different intervention
strategies. The figure shows contact tracing (CT) is the most cost-effective
over both self-quarantine (SQ) and vaccination (VACC); excluding $0 cost for
no-intervention (NI)

In this section, we evaluate the economic implications of various
interventions in controlling the pandemic. The cost of the no-intervention
(NI) case is $0. For the self-quarantine (SQ) and contact tracing (CT)
interventions, we account for the cost of tests taken by agents experiencing
COVID-19 symptoms. The average cost per test for each case is assumed to be $5
Du et al. (2021). We assume this is the average cost per testing kit incurred
by the government. Similarly, for vaccination (VACC), each dose is priced at
an average of $20 Kates et al. (2023).

Figure 5 shows the respective costs of each intervention strategy, with their
individual impacts elaborated in Section 4.1. 4.1. Computing the total
expenditure, VACC stands at $1.02M, SQ at $0.54M, and CT at a minimum of
$0.42M Beyond the reduction in infections and hospitalizations explored in
Section 4.1, it’s evident that CT surpasses by being 23% and 59% more cost-
effective than SQ and VACC, respectively.

Figure 6. Comparative analysis of hospitalizations under a fixed budget of
$0.42M for contact tracing (CT) versus vaccination (VACC). The figure shows CT
leads to a significant reduction in hospitalizations compared to VACC along
with a pronounced delay in the peak, underlining the superior cost-
effectiveness and strategic value of contact tracing in the pandemic’s early
stages.

Further, for a fixed budget of $0.42M, our analysis shows that deploying
contact tracing with self-quarantine (CT) outperforms an exclusive focus on
vaccination. In this context, the CT strategy remains consistent with the
previous simulations, with only the daily vaccination production adjusted to
fit the budget. As Figure 6 demonstrates, allocating the budget to testing
with contact tracing (CT) results in a significant 63% decline in peak
hospitalizations against the no-intervention (NI) baseline. Conversely,
directing the entire same budget towards vaccinations alone (VACC) yields just
a 32% reduction in peak hospitalizations compared to NI. Notably, while the
VACC and NI peaks coincide, the CT approach introduces a 13-day delay in the
surge of hospitalizations. This 20% temporal divergence is pivotal, offering
healthcare systems a crucial extended window for preparation.

In conclusion, for every dollar invested, contact tracing proves to be the
more cost-efficient choice compared to vaccination, particularly in the
crucial first 100 days. A mere 40% app adoption rate paired with 80% self-
quarantine compliance under the CT strategy offers a better return on
investment than the same expenditure on vaccination alone.

###  4.4. Coupled effect of pharmaceutical, behavioral, and digital
interventions

Figure 7. Analysis of interplay of digital and behavioral interventions on
delayed vaccination. (a) Illustrates the impact of vaccine deployment speed on
hospitalizations. Vaccine rollout delays lead to a consequential rise in
hospitalizations with peak incidence remaining consistent. (b) Demonstrates
the synergy of contact tracing and varied vaccine deployment timings,
emphasizing that combining VACC(t = 30) + CT significantly diminishes
hospitalizations and prolongs the time to peak compared to early vaccination
alone. (c) Indicates the challenges with vaccine initiation at the pandemic’s
zenith, stressing that even late vaccine rollouts, when coupled with testing,
contact tracing, and self-quarantine, can drastically mitigate infections and
allow for a crucial extended immunization period. This highlights the
indispensability of integrating behavioral and digital strategies, especially
in the pandemic’s early days when clinical interventions might not yet be in
full swing.

In this section, we study the combined effects of vaccine deployment speed and
other pivotal interventions, examining their collective impact on
hospitalizations. We observe that regardless of intervention combinations, the
peak consistently emerges within the first 100 days, highlighting the
significance of timely informed decisions. Figure 7(a) illustrates the
relationship between the speed of vaccine deployment at distinct time
intervals: $t=10$, $t=30$, and $t=60$ and the subsequent hospitalizations.
Compared to starting the vaccinations at t=10, a delayed vaccination drive
starting at t=30 and t=60 increases the number of hospitalizations by 61% and
103%, respectively, with all scenarios peaking around the same time.

However, by integrating other digital and behavioral interventions with
vaccination, we observe a transformative mitigation effect. Figure 7(b) shows
that VACC starting at t = 30 + CT leads to a 55% reduction in hospitalizations
compared to only early vaccination starting at t=10 and further a 72% drop in
hospitalizations compared with VACC at t=30. Additionally, this amalgamated
approach grants an extra 14-day buffer prior to the hospitalization peak,
facilitating a strategic advantage for healthcare system preparedness. The
cost analysis for Figure 7(b) is provided in supplementary material.

Further, sole reliance on late vaccination starting at $t=60$ fails because of
the inherent lag in post-inoculation immunity development. However, when this
late vaccination is augmented with proactive contact tracing and self-
quarantine measures, the results are noteworthy: a 61% reduction in
hospitalizations accompanied by an additional 23-day window for effective
immunization as in Figure 7(c).

This underscores the potential of non-pharmaceutical interventions (NPIs) like
behavioral and digital, not just as alternate measures but as pivotal
strategies in pandemic control, especially when vaccination rollout faces
delays. Thus, a multifaceted approach combining behavioral, digital, and
pharmaceutical measures is pivotal in effectively managing the pandemic,
especially during the first 100 days when clinical interventions face delays.

###  4.5. Geographical spread

Figure 8. Geographical progression of infections in Kings’s County,
Washington, at different time intervals. (Top) In case of no intervention, the
infection spreads to 25% of the population by t=50, 76% by t=70, and 81% by
t=120. (Bottom) In the case of combined digital, behavioral, and
pharmaceutical interventions, infection spreads slowly to only 5% of the
population by t=50, 19% by t=70, and only 36% by t=120

Figure 8 shows heat maps of infection spread over time in King’s County,
Washington State at distinct time intervals: $t=50$, $t=70$, and $t=120$. We
compare the unmitigated (NI) scenario in Figure 8 (Top) against an integrated
strategy that combines all interventions vaccinations, testing, contact
tracing, and self-quarantine in Figure 8 (Bottom). We observe that in the case
of no intervention, the infection spreads aggressively, already infecting a
substantial 25% of the population by day 50, 76% by t=70, and 81% by t=120. In
stark contrast, Figure 8 (Bottom) captures the attenuated spread when a
comprehensive set of interventions is deployed. Infections stand at a mere 5%
population infected by day 50, 19% by day 70, and only 36% by t=120.

##  5\. Discussion

In this paper, we highlight the potential of agent-based models to simulate
highly complex environments through multiple intertwined interventions. We
discussed intricate modeling of pharmaceutical, behavioral, and digital
interventions and how their holistic understanding is important when creating
pandemic policies. While we take one step towards bridging the gap between
understanding the emerging trends and policy-making, we posit that there can
be additional implicit factors stemming from complex interventions and their
ripple effects that frequently go unnoticed, yet significantly influence the
trajectory of the pandemic. For instance, financial interventions like
severance funds or government aid Institute ([n. d.]) provided to the
unemployed to stay at home could alter mobility patterns Askitas et al.
(2021); Alessandretti (2022), influencing the pandemic’s course. Additionally,
our cost analysis focuses predominantly on explicit monetary costs. Some
interventions, while not incurring direct costs, may lead to broader economic
implications McKee and Stuckler (2020); Verschuur et al. (2021a); Shang et al.
(2021). For instance, extensive lockdowns, a common strategy during COVID-19,
triggered a severe global economic downturn. This collapse was characterized
by soaring unemployment rates Ahmad et al. (2023); Antipova (2021), halted
international trade Verschuur et al. (2021b); Hayakawa and Mukunoki (2021);
Liu et al. (2022), and suspended supply chains Naseer et al. (2023); Guan et
al. (2020); Magableh (2021); Paul et al. (2021). These influencing factors
further raise pivotal questions for policy-making: Does the amount of
unemployment aid play a larger role in pandemic control than the speed of its
provision? Are short-term lockdowns (¡31 days) the solution Yamaka et al.
(2022); Oraby et al. (2021); Bisiacco and Pillonetto (2021), or is there an
optimal percentage of people returning to offices (RTO) Yang et al. (2022);
Garzillo et al. (2022) that can help control the pandemic and also not harm
the economy at a global scale?

Answering these questions can provide essential insights into the efficacy and
promptness of policy interventions. Therefore, modeling these latent factors
is a vital future direction in aiming for a comprehensive understanding of a
pandemic’s broader impacts. This will guide us toward more nuanced policy-
making for future outbreaks, ensuring both public health and economic
stability.

##  6\. Conclusion

In this paper, we emphasize the capabilities of agent-based models in
understanding the complex dynamics of pandemics and simulating the potential
impact of different policy interventions. By simulating interventions with
their real-world deployment challenges, we analyze emergent behaviors on
populations at scale. Our approach goes beyond merely evaluating standalone
interventions by capturing the comprehensive interplay of combined strategies.
From our experiments, several critical findings emerged. The initial 100 days
of a pandemic largely shape its course and underline the need for swift and
informed decisions from the beginning. While vaccines play a pivotal role in
reducing individual susceptibility, achieving community-wide immunity is a
gradual process due to the time-consuming nature of mass vaccination rollouts.
Our research emphatically highlights the indispensability of sustained
interventions alongside vaccinations. Notably, we observed contact tracing’s
efficacy for not only reducing the cumulative infections from 81% (in the
absence of intervention) to 54% but also delaying the infection peak by 14
days. Our analysis further shows that the same amount of dollars spent on
extensive testing with contact tracing and self-quarantine proves to be more
cost-effective than spending on vaccinations alone. Future global health
crises thus necessitate a balanced, multi-pronged response.

##  7\. Supplementary material

###  7.1. More details on the simulation framework

Transition Mechanics: Our ABM’s transition mechanics dictate the chronological
progression of every agent’s state variables in the system, contingent upon
the agents’ actions. Among these variables, the evolution related to testing,
self-quarantine, and vaccination is driven by individual agent actions.
However, the progression of the agent’s stage is nuanced and draws from the
model described in Hinch et al. (2021). The stage dynamics, which are modified
SEIR dynamics at the agent level, can be divided into two parts: (i) Infection
dynamics: This segment addresses the state transition from susceptibility to
either the asymptomatic or the pre-symptomatic infectious states. The process
aggregates the outcomes of interactions with all other agents, factoring in
the quarantine and vaccination states of these agents. This is a Markovian
transition each phase presents a probability wherein an agent transitions from
a non-infected susceptible state to an infectious one. The potency of each
interaction varies based on factors like age, disease phase, quarantine,
vaccination status, and the facilitating interaction network. The likelihood
of infection results from aggregating the influencing factors from every
interaction. (ii) Disease dynamics: This section navigates through the various
infectious disease stages, culminating in either recovery or a death-absorbing
state. These shifts are semi-Markov in nature, where durations are inferred
from continuous-time distributions, influenced by disease stage and age
parameters.

###  7.2. Cost analysis of delayed vaccine

Figure 9 shows the cost analysis for different interventions including
vaccination starting at times t=10, 30, 60, and combined intervention of
vaccination at t=30 with contact tracing. For each case, once the vaccination
rollout begins, 0.3% of the population is inoculated daily. The total cost for
VACC 30 + CT includes the cost of vaccines and tests for contact tracing,
which is higher than the cost of administering vaccines alone starting at
t=10, t=30, or t=60. More details on the impact of each of these interventions
are covered in Section 4.4.

Figure 9. Cost analysis of behavioral and digital interventions with delayed
vaccination (VACC+CT). Further explained in Section 4.4

###  7.3. Sensitivity Analysis

We also perform sensitivity analysis of some parameters including app adoption
rate, self-quarantine compliance probability on receiving exposure
notification in contact tracing, and efficacy of the first dose of vaccination
on hospitalizations, cumulative infections, and cost of containing the
pandemic as shown in Figures 10, 11, and 12.

Figure 10. Sensitivity analysis of the impact of app adoption in contact
tracing on hospitalizations, cumulative infections, and the cost of deployment
for pandemic containment

Figure 11. Sensitivity analysis of self-quarantine compliance probability in
contact tracing on hospitalizations, cumulative infections, and the cost of
deployment for pandemic containment

Figure 12. Sensitivity analysis of the efficacy of the first dose of
vaccination on hospitalizations, cumulative infections, and the cost of
deployment for pandemic containment

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