Berks County Medical Society Medical Record Summer 2020 - 39

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s the COVID-19 pandemic has overwhelmed global
health systems and caused the loss of so many souls, many
countries have responded with dramatic intervention
measures to contain the virus. The COVID-19 pandemic and
these preventive measures have dominated the news media for
several months. Policymakers and the public have been discussing
whether the economy should be opened, if so when, or effectiveness
of interventions, such as stay-at-home orders, social distancing
measures, and preventive testing. Decision-makers at various
levels of the government, as well as private/public organizations,
have to make such critical decisions that have a profound effect
on the well-being of individuals and society. Policymakers have
been increasingly relying on epidemiological models to guide their
decisions and communicating their policy choices to the public
through visual aids created by these models. Through various
media outlets, the public has seen graphs illustrating the spread of
COVID-19 and learned the concept of "flattening the curve" so
that our healthcare providers have the adequate resources needed to
treat COVID-19 patients without being overwhelmed. In this short
article, we will first briefly introduce the underlying mathematical
principles of these epidemiological models and then demonstrate
how these models can inform the decision-making processes for
devising containment measures of COVID-19 using an agent-based
simulation (ABS) model that we recently developed.
Mathematical models that represent the diffusion of an
infectious disease in a population have been around for a long
time. We can broadly group these models into two categories:
system dynamic mathematical models and simulation models.
Daniel Bernoulli developed the first mathematical epidemiological
model in 1766 to study smallpox mortalities [1]. Bernoulli divided
the population into two groups, the susceptibles (those who have
not been infected yet) and the immunes (those who have been
immunized after one infection), and then defined the mathematical
equations to represent the transition rate of individuals from the
susceptible to the immune group. In the late 1920s, Kermack and
McKendrick introduced the Susceptible-Infected-Recover (SIR)
model [2], which is the foundation of many other epidemiological
models used today. The SIR model assumes that individuals go
through three sequential states: susceptible (S) to the disease,
infected (I), and then either recovered (R) or died (Figure 1). In the
SIR model, the transition rate ß at which the susceptible individuals
become infected is proportional to the number of their contacts
with infected individuals, and the transition rate y from infected to
recovered depends on the attributes of the disease. This notion of
contact among individuals makes the SIR model a good candidate
to analyze the spread of viruses such as COVID-19.

Figure 1. The states of the SIR Model

Simulation models aim to replicate the real-world on a
computer using statistical methods to represent how individuals
pass the virus to others. While pure mathematical models are
holistic, simulation models can incorporate many details such as
individuals' actual interactions, population mobility, capacities
of health providers, health conditions of different demographical
groups, etc. The simulation model introduced in this article is an
ABS model,
which represents the state-of-the-art in mathematical epidemiology
today [3].

Agent-Based Simulation Models
In computer science, an agent is an autonomous computing unit
that receives input from its environment, makes semi-intelligent
decisions by processing the input, and takes independent actions
towards achieving its goals. An agent could be as simple as a
thermostat or as complex as an autonomous vehicle. An ABS model
includes thousands of agents residing in a virtual environment.
These agents interact with one another and the environment while
they act in a way to achieve their individual goals. From these
individual actions of the agents, a complex behavior of the whole
system emerges. We observe such complex system behaviors in our
daily lives, such as stock markets, traffic congestion, and flocking of
swarms in nature.
To predict the spread of a virus in a population when data
is limited, ABS models usually extend the SIR framework by
considering an interaction network of individuals. Therefore,
ABS models can be used in the early stages of a pandemic. For
example, the ABS model developed by a team at Imperial College
London [4] predicted that the pandemic would overwhelm health
systems in a short time with 250,000 estimated deaths in Great
Britain and 1.1-1.2 million in the US. These predictions attracted
the attention of policymakers as well as the public [5]. A key
input parameter to a SIR-based simulation model is the basic
reproduction number (R0), which represents the average number
of people to whom an infected individual will pass the virus. R0
determines the rate of transition from the state S to the state I.
Other parameters of the SIR model include the disease incubation
time, the duration of the disease, and the time to recover. Although
SIR-based simulation models are quite simple, researchers have been
able to closely approximate the reported number of COVID-19
cases in the UK and Italy using R0 values between 2.25 and 2.75 [6].

Description of the ABS Model
Compared to pure mathematical models, the main advantage
of ABS models is the flexibility of incorporating complex logic and
more realistic scenarios. Based on the SIR model, we have developed
a simulation model given in Figure 2 to study the impact of social
distancing measures and the availability of testing on the spread of
COVID-19. Our main goal is to demonstrate how an ABS model
can support policymakers in their decision making. We will first
briefly describe our ABS model and then explain its use cases to
guide decision making.
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SUMMER 2020

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39
Berks County Medical Society Medical Record Summer 2020

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