Capstone Project Report

AGENT-BASED DISEASE MODELLING

December 18, 2024

Elvia Dey & Karan Kumar

Ashoka University
Department of Computer Science
Report on Capstone Project under the supervision of
Professors Debayan Gupta and Sandeep Juneja
Acknowledgement
We would like to express our deepest gratitude to our supervisors, Professors Debayan Gupta and Sandeep
Juneja, for their guidance and support throughout this semester. Their insights and encouragement have
been instrumental in the successful completion of this capstone project.

A special thanks to Phillip Cherian from the Physics Department, whose expertise was crucial to our un-
derstanding and progress of the project. His consistent support through weekly meetings and detailed
explanations helped clarify the complexities of this project.

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Contents
1 Introduction 4

2 Motivation 4

3 Background 5
3.1 Compartmental Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.1 SIR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.2 SAIR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1.3 SEIR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Agent-Based Modeling (ABM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2.1 Stochastic Transitions in ABM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2.2 Stochastic SIR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2.3 Comparing Stochastic and Deterministic SIR . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Network Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3.1 Household and Workplace Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3.2 Testing Network Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Literature Survey 12

5 Problem Statement/Objectives 13

6 Model and Population Dynamics 14

6.1 General Population (Non-MSM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.2 MSM Subpopulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.2.1 Attributes and Network Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.2.2 Rationale for Heavy-Tailed Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6.2.3 Infection Dynamics within the MSM Network . . . . . . . . . . . . . . . . . . . . . . . 15

7 Sensitivity Analysis of Beta and Mu 16

7.1 Experiment 1: Initial Infection in MSM Network . . . . . . . . . . . . . . . . . . . . . . . . . 16
7.1.1 Analysis and Discussion: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
7.2 Experiment 2: Initial Infection in Non-MSM Population . . . . . . . . . . . . . . . . . . . . . 17
7.2.1 Analysis and Discussion: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.3 Experiment 3: Workplace Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.3.1 Analysis and Discussion: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

8 Intervention Strategies 19
8.1 Aggressive Vaccination Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.2 Testing and Contact Tracing Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.3 Behavioral Change Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.4 Combined Strategy (Moderate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.5 Combined Strategy (Aggressive) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
8.6 Early Intervention Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8.7 MSM-Focused Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

9 Key Observations 26

10 Conclusions 26

11 Extensions and Future Work 26

12 References 27

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1 Introduction
The 2022 monkeypox outbreak, largely concentrated among men who have sex with men (MSM), showed the
need for epidemiological models that accurately represent real-world contact patterns. This report uses an
agent-based model (ABM) to investigate monkeypox spread within a heavy-tailed sexual contact network,
characteristic of MSM populations. ABMs offer a more nuanced approach than traditional compartmental
models by simulating individual-level interactions and behaviors.

Our model simulates transmission within a synthetic population structured by households, workplaces, and
an MSM sexual contact network generated using a Weibull distribution, reflecting empirical data on the
heterogeneous distribution of sexual partnerships. We present results from three experiments exploring the
impact of varying initial outbreak conditions and transmission probabilities. These experiments consider
different initial infection locations (MSM or non-MSM population) and incorporate workplace transmis-
sion to assess its influence. By analyzing the resulting epidemic curves, this research provides insights into
how heavy-tailed networks shape monkeypox dynamics and can inform targeted public health strategies for
controlling similar outbreaks.

2 Motivation
The 2022 monkeypox outbreak, disproportionately affecting men who have sex with men (MSM), highlighted
the critical need to understand disease transmission within complex sexual networks. The concentrated
spread within this community, coupled with the heterogeneous nature of sexual partnerships, motivated this
project to explore the role of heavy-tailed contact networks in shaping the outbreak’s dynamics.

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3 Background
3.1 Compartmental Models
We started by implementing traditional deterministic compartmental models, including SIR, SAIR, and
SEIR, to model disease spread. Each of these models divides the population into distinct compartments (e.g.,
Susceptible, Infected, Recovered) and uses ordinary differential equations (ODEs) to simulate transitions
between compartments based on specific parameters. These models helped us understand the basic dynamics
of disease spread under well-mixed assumptions.

3.1.1 SIR Model

The SIR model is defined by three compartments: Susceptible (S), Infected (I), and Recovered (R). The rate
of change for each compartment is governed by parameters like infection rate and recovery rate, as outlined
in the differential equations:
dS λs
= − SI (1)
dt N
dI λs
= SI − λi I (2)
dt N
dR
= λi I (3)
dt

Figure 1: Well-mixed solution to the SIR model

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3.1.2 SAIR Model
The SAIR model extends the SIR model by adding an asymptomatic (A) compartment. Infected individuals
who do not show symptoms are classified as asymptomatic but can still spread the disease. The differential
equations governing the transition between compartments for SAIR are:
dS λs
= − S(A + I) (4)
dt N
dA λs
= γ S(A + I) − λA A (5)
dt N
dI λs
= (1 − γ) S(A + I) − λI I (6)
dt N
dR
= λA A + λI I (7)
dt

Figure 2: Well-mixed solution to the SAIR model

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3.1.3 SEIR Model
The SEIR model adds an Exposed (E) compartment to account for individuals who have been exposed to
the disease but are not yet infectious. The differential equations for the SEIR model are:
dS SI
= λS (8)
dt N
dE SI
= λs − λE E (9)
dt N
dI
= λE E − λI I (10)
dt
dR
= λI I (11)
dt

Figure 3: Well-mixed solution to the SEIR model

3.2 Agent-Based Modeling (ABM)

The next step involved implementing agent-based models (ABM) to simulate individual-level disease dynam-
ics, allowing for heterogeneity and more realistic interactions between agents. In ABM, agents (representing
individuals) are assigned unique attributes, such as health status, and move between different locations, such
as home and workplace.

3.2.1 Stochastic Transitions in ABM

In our agent-based simulations, we introduced stochastic transitions. Each agent has a probability of moving
from one compartment to another (e.g., from Susceptible to Infected) based on the interaction rate with other
agents. These transitions were modeled as probabilities, and the simulation ran for 100 iterations to capture
the variability in outcomes.

3.2.2 Stochastic SIR Model

In a stochastic SIR model, we compute the transition probabilities for each agent at each timestep ∆t:
I
pSI = λS ∆t (12)
N

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 pIR = λI ∆t (13)
These equations define the probabilities for a susceptible agent transitioning to infected, and an infected
agent recovering. We ran 100 simulations to capture the variability in outcomes and plotted the results.

Figure 4: Stochastic solution to the SIR model

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3.2.3 Comparing Stochastic and Deterministic SIR

Comparing the average of 100 stochastic runs with the deterministic solution for the SIR model, we got the
following result:

Figure 5: Comparison of deterministic and stochastic solutions for the SIR model

The peak for the stochastic model is lower than the deterministic model because in the former, the
infection dies out if fewer than one person is infected, whereas in the deterministic model, the disease
continues spreading as long as I > 0, i.e., even if I is very low. This leads to a lower average peak in the
stochastic model, as some runs result in the disease dying out.

3.3 Network Structure

To enhance realism, we introduced a network structure where agents move between specific locations (home
and workplace) at each timestep. Each agent’s transition probabilities are based on the number of susceptible,
infected, and recovered individuals at that location.
The steps for running the network structure include:

1. Assigning states (S, I, R) to each agent.

2. Updating agent locations based on their schedule (Home, Work).

3. Looping over each location and updating transition probabilities based on the number of agents at
each location.

4. Transitioning agents based on location-specific probabilities.

5. Repeating until all agents recover or the total time elapses.

We ran 20 simulations with a population of 100,000 agents and confirmed the network structure works as
expected.

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 Figure 6: Simulation of network structure in Julia

3.3.1 Household and Workplace Distributions

We modeled households with an average of 4 people per household, leading to a Poisson distribution of agents
across households. Similarly, workplaces were modeled with 50 agents per workplace. Both distributions
were verified through visualizations.

Figure 7: Distribution of agents across households

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 Figure 8: Distribution of agents across workplaces

3.3.2 Testing Network Structure

To validate the network structure, we set the number of houses and workplaces to 1. The results showed
that the network structure was implemented successfully, as it matched the behavior of the stochastic SIR
model (well-mixed model).

Figure 9: Validation of the network structure

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4 Literature Survey
Our aim is to investigate the dynamics of monkeypox spread within heavy-tailed sexual contact networks,
a crucial area of inquiry given the observed concentration of the 2022 outbreak among men who have sex
with men (MSM). Understanding how network structure influences transmission is essential for developing
effective control strategies. The following studies provide context and motivation for our work:
1. Heavy-tailed sexual contact networks and monkeypox epidemiology in the global out-
break, 2022 (Endo et al., 2022): This study serves as the primary foundation for our project.
Endo et al. demonstrate the significant role of heavy-tailed sexual partnership distributions in driv-
ing and sustaining the monkeypox outbreak among MSM. They utilize a Weibull distribution, fitted
to empirical partnership data from the National Surveys of Sexual Attitudes and Lifestyles (Natsal),
to model this network structure and show that even a small number of highly connected individuals
can significantly amplify transmission. Our research builds directly on this framework, incorporating
a similar heavy-tailed network structure to explore disease progression and the efficacy of potential
interventions.
2. Modeling the Impact of Sexual Networks in the Transmission of Monkeypox virus Among
Gay, Bisexual, and Other Men Who Have Sex With Men – United States, 2022 (Spick-
nall et al., 2022): This research underscores the importance of considering different partnership
types (main, casual, one-time) in modeling monkeypox transmission. Spicknall et al. reveal that one-
time partnerships, while less frequent, contribute disproportionately to transmission, highlighting the
heterogeneity of contact patterns within MSM networks. This finding emphasizes the need for nu-
anced models that capture the diversity of sexual interactions, aligning with our focus on heavy-tailed
networks, which inherently represent such heterogeneity.
3. Community transmission of monkeypox in the United Kingdom, April to May 2022 (Vi-
vancos et al., 2022): This report offers a detailed description of the early outbreak dynamics in
the UK, emphasizing the prominent involvement of the MSM community and the challenges associ-
ated with contact tracing in these networks. The observation of rapid spread within interconnected
sexual networks motivates the use of network-based models, like ours, which explicitly simulate the
transmission dynamics along contact links.

4. Maximizing the impact of limited vaccine supply under different early epidemic condi-
tions: a 2-city modelling analysis of monkeypox virus transmission among men who have
sex with men (Knight and Tan, 2022): This study tackles the practical challenge of optimizing
vaccine allocation with limited supply in the context of interconnected MSM networks. By considering
factors like network size and R0, Knight and Tan demonstrate the complex interplay between network
characteristics and optimal vaccine prioritization. This work reinforces the importance of understand-
ing how network topology, specifically the heavy-tailed nature of sexual contact networks as highlighted
by Endo et al. (2022), influences the effectiveness of vaccination and other intervention strategies.

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5 Problem Statement/Objectives
The 2022 monkeypox outbreak showed the need for epidemiological models that accurately reflect real-world
contact patterns and transmission dynamics, particularly within the men who have sex with men (MSM)
community. The project focuses on the following objectives:

1. Model Development and Validation: To develop and validate a stochastic agent-based model that
simulates monkeypox transmission within a heavy-tailed MSM sexual contact network, incorporating
household and workplace interactions. This model will consider both sexual transmission within the
MSM network and general transmission (applicable to all individuals) within households and work-
places.

2. Impact of Initial Conditions: To investigate the influence of differing initial outbreak conditions
on the epidemic trajectory. Specifically, we compare scenarios with:
(a) An initial infection solely within the MSM network.
(b) An initial infection solely within the non-MSM population.
(c) An initial infection within the non-MSM population combined with a low probability of workplace
transmission.
3. Sensitivity Analysis of Transmission Parameters: To analyze the sensitivity of the model out-
comes to variations in key transmission parameters, namely:
• β (beta): Representing the probability of transmission per contact.
• µ (mu): Representing the contact probability within the MSM sexual network.

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6 Model and Population Dynamics
6.1 General Population (Non-MSM)
The model simulates a population of 10,000 individuals, designed to represent a simplified yet structured
society. Each individual is treated as an independent agent within the model and is characterized by the
following attributes:
• Health Status: Each agent is assigned an initial health status: Susceptible (S), Exposed (E), Infected
(I), or Recovered (R). This is determined by the initial parameters of the simulation, where most agents
start as susceptible, and a small number are infected to initiate the outbreak.
• Age: Agents are assigned an age drawn from a truncated normal distribution, with a mean of 45 and a
standard deviation of 15, constrained between 0 and 100 years. This distribution is chosen to represent
a realistic age spread within a population, acknowledging that susceptibility and behavior can vary
with age.
• Location Assignments: A crucial aspect of the model is the simulation of daily interactions through
the assignment of agents to households and workplaces. Households are designed to have an average of
4 people, while workplaces have an average of 50. These assignments are stochastic, based on Poisson
distributions, reflecting the natural variation in household and workplace sizes.
• Daily Schedule: The model simulates a daily routine where agents spend half a day at their assigned
home and half a day at their workplace. This movement between locations is a critical component
for modeling disease transmission, as it simulates the regular mixing of individuals in different social
contexts.
Infection dynamics within the general population are primarily driven by interactions within households
and workplaces. The probability of a susceptible individual becoming exposed is calculated for each loca-
tion, based on the number of infected individuals present. The model incorporates a reduced transmission
probability in workplaces compared to homes, reflecting potential differences in interaction types and dura-
tions. These parameters are crucial for calibrating the model to reflect realistic infection scenarios within
the general population.

6.2 MSM Subpopulation

The model identifies a subset of the population as MSM, constituting 1% of adult men. This proportion is in
line with estimates from various studies and is particularly relevant for modeling the monkeypox outbreak,
given its observed higher prevalence in this group (Endo et al., 2022). The MSM subpopulation is crucial
for understanding the dynamics of the current monkeypox outbreak, as it exhibits distinct characteristics
compared to the general population.

6.2.1 Attributes and Network Structure

MSM agents share the basic attributes of the general population but have additional characteristics related
to their sexual contact network:
• MSM Status: Each agent is designated as either belonging to the MSM subpopulation or not. This
is determined during the initialization phase, where adult male agents are randomly sampled to be
part of the MSM group.
• MSM Contacts: A defining feature of MSM agents is their network of sexual contacts, represented by
a list of other MSM agents. This network is constructed using a Weibull distribution, chosen to reflect
the heavy-tailed nature of sexual partnership distributions observed in empirical studies, particularly
among MSM (Endo et al., 2022).

The model introduces a parameter, µ, representing the probability of an MsM individual gettting
exposed during an encounter. This parameter is varied in simulations to assess its impact on disease
spread.

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6.2.2 Rationale for Heavy-Tailed Networks
The decision to employ a heavy-tailed distribution, specifically the Weibull distribution, for modeling the
MSM sexual contact network is central to the project’s methodology. This approach is supported by:
1. Empirical Evidence: Studies on sexual partnership distributions, especially within the MSM com-
munity, consistently reveal a heavy-tailed pattern. This indicates that a small number of individuals
have a significantly large number of partners, while most have fewer partners (Endo et al., 2022). The
Natsal data provides empirical support for this pattern.
2. Limitations of Alternative Distributions: While other heavy-tailed distributions like the Pareto
distribution exist, they can lead to unrealistic scenarios with individuals having an excessively high
number of partners, potentially skewing results. The Weibull distribution offers a more realistic model
of heavy-tailed networks, avoiding these unphysical features.
3. Relevance to Monkeypox Transmission: The heavy-tailed nature of the MSM network signifi-
cantly impacts monkeypox transmission. Individuals with many partners serve as hubs, increasing the
likelihood of both acquiring and transmitting the infection. This heterogeneity in contact patterns
can result in rapid and sustained transmission within the MSM community, a pattern observed in the
current outbreak (Endo et al., 2022).

Figure 10: Heavy-tailed MSM Sexual Contact Network

6.2.3 Infection Dynamics within the MSM Network

Infection within the MSM network occurs through two main pathways:
1. Location-Based Exposure: Similar to the general population, MSM agents can be exposed through
interactions at their assigned locations (home and work). The same probability calculations based on
the number of infected individuals at each location apply.
2. Contact Network Exposure: MSM agents can also be exposed through contact with infected
partners in their sexual network. The probability of transmission is influenced by the parameter ‘mu‘.
The model simulates contact events within the network, where if one individual is infected and the
other susceptible, there is a probability of transmission.

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7 Sensitivity Analysis of Beta and Mu
7.1 Experiment 1: Initial Infection in MSM Network
This experiment simulates an outbreak starting with a single infected MSM individual (and 0 non-MSM
infections), exploring how the disease spreads from the MSM population into the broader community under
different transmission probabilities. We considered five values for µ: 0.2, 0.4, 0.6, 0.8, and 1.0. Each scenario
was simulated for 100 runs to capture the stochastic nature of the spread. The β value used for these
simulations were 0.1, 0.2, ..., 0.5, representing each row of the figure.

7.1.1 Analysis and Discussion:

The simulations revealed several key patterns:
• Created a single peak pattern in the overall infection curve

• MSM population exhibited an earlier infection peak

• General population peak occurred later in time
• MSM peak showed relative independence from household infectivity (β)

• Both MSM and general population peaks demonstrated strong dependence on sexual transmission
probability (µ)
• Resulted in lower overall outbreak size compared to other scenarios

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7.2 Experiment 2: Initial Infection in Non-MSM Population
This experiment explores the reverse scenario: the outbreak begins with 50 infected non-MSM individuals
(and 0 MSM infections), investigating the penetration of the infection into the MSM network. We again
varied µ across the same five values and ran 100 simulations for each scenario. The β value used for these
simulations were 0.1, 0.2, ..., 0.5, representing each row.

7.2.1 Analysis and Discussion:

The results showed distinct characteristics:
• Generated a clear two-peak pattern in disease spread
• First peak: Dominated by non-MSM population spread

• No observable dependence on sexual transmission probability (µ) during first peak

• Second peak: Emerged when infection entered MSM network
• Strong dependence on µ during second peak
• Required higher initial number of infections to achieve comparable outbreak sizes

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7.3 Experiment 3: Workplace Transmission
This experiment introduces an additional layer of complexity by incorporating a small probability of work-
place transmission (1% of the household transmission probability), which was set to 0 in the previous
experiments. This adds a potential bridge for infection between MSM and non-MSM individuals beyond
household contacts. This experiment is performed for the first two values of µ used in experiment 2. This
demonstrates the extent to which stochasticity can affect the spread of the disease when coupled with in-
creased inter-network transmission, an important feature of real-world contact networks.

7.3.1 Analysis and Discussion:

The introduction of workplace transmission revealed important effects:
• Amplified the patterns observed in Experiment 2

• Maintained two distinct peaks in infection spread

• Produced higher overall case numbers
• Generated longer tail of infections
• Workplace transmission (even at 1% of household rate) significantly enhanced spread

• Created more sustained transmission chains

• Further emphasized the two-peak behavior in disease progression

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8 Intervention Strategies
We start with the initial conditions of the third experiment and employ the following intervention strategies.

8.1 Aggressive Vaccination Campaign

This strategy focuses on rapidly vaccinating the population to achieve herd immunity quickly.

Agent Behavior: Agents have a 5% chance of being vaccinated each day. Once vaccinated, they have
an 85% reduced chance of becoming infected upon exposure.

• enable_vaccination = true

• vaccine_deployment_rate = 0.05 (5% of the population vaccinated per day)

• vaccine_efficacy = 0.85 (Vaccine is 85% effective, reducing infection chance upon exposure)

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8.2 Testing and Contact Tracing Focus
This strategy emphasizes widespread testing to identify infected individuals and then tracing their contacts
to isolate them and prevent further spread.

Agent Behavior: Agents get tested every 3 days. If an agent tests positive (with 95% accuracy), they
enter quarantine. Additionally, 90% of their contacts are traced and also placed in quarantine.

• enable_testing = true

• testing_sensitivity = 0.95 (95% accurate tests, determining if an infected agent is correctly iden-
tified)
• default_testing_frequency = 3 (Testing every 3 days)
• contact_tracing_efficiency = 0.9 (90% of an infected agent’s contacts are successfully traced and
quarantined)

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8.3 Behavioral Change Campaign
This strategy relies on informing the public about the risk of infection, leading to behavioral changes that
reduce transmission.

Agent Behavior: When the number of infected agents exceeds 50, all agents increase their risk aware-
ness by 20% (up to a maximum of 100%). This increased awareness leads to a 10% reduction in their contact
rate (also up to a maximum of 100% reduction).

• enable_risk_communication = true
• risk_threshold = 50 (Awareness campaign triggered when 50 agents are infected)
• awareness_increase = 0.2 (20% increase in risk awareness, reducing susceptibility)
• behavior_change_rate = 0.1 (10% reduction in contact rate due to increased awareness)

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8.4 Combined Strategy (Moderate)
This strategy combines vaccination, testing, contact tracing, and risk communication at moderate levels.

Agent Behavior: Agents have a 2% chance of being vaccinated daily. They are tested weekly, and if
positive, they and 80% of their contacts are quarantined. When infections exceed 100, risk awareness in-
creases by 10%, leading to a 5% reduction in contact rates.

• enable_vaccination = true

• vaccine_deployment_rate = 0.02 (2% of the population vaccinated per day)

• enable_testing = true
• default_testing_frequency = 7 (Weekly testing)

• contact_tracing_efficiency = 0.8 (80% contact tracing efficiency)

• enable_risk_communication = true
• risk_threshold = 100 (Risk communication triggered at 100 infected agents)
• awareness_increase = 0.1 (10% increase in awareness)

• behavior_change_rate = 0.05 (5% reduction in contacts)

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8.5 Combined Strategy (Aggressive)
This strategy is similar to the moderate combined strategy but with more aggressive parameters, leading to
stronger effects on agent behavior.

Agent Behavior: Agents have a 5% daily chance of vaccination. They are tested every 3 days, and
if positive, they and 90% of their contacts are quarantined. When infections exceed 50, risk awareness
increases by 20%, leading to a 10% reduction in contact rates.

• enable_vaccination = true
• vaccine_deployment_rate = 0.05 (5% of the population vaccinated per day)
• enable_testing = true
• testing_sensitivity = 0.95 (95% test accuracy)

• default_testing_frequency = 3 (Testing every 3 days)

• contact_tracing_efficiency = 0.9 (90% contact tracing efficiency)
• enable_risk_communication = true

• risk_threshold = 50 (Lower threshold for triggering awareness)

• awareness_increase = 0.2 (20% increase in awareness)
• behavior_change_rate = 0.1 (10% reduction in contacts)

23
8.6 Early Intervention Strategy
This strategy aims to intervene very early in the outbreak, even with a small number of cases, using a
combination of measures.

Agent Behavior: Agents have a 3% daily chance of vaccination. They are tested every 5 days, and
if positive, they and 85% of their contacts are quarantined. When infections exceed 25, risk awareness
increases by 15%, leading to an 8% reduction in contact rates.

• enable_vaccination = true
• vaccine_deployment_rate = 0.03 (3% of the population vaccinated per day)
• enable_testing = true
• default_testing_frequency = 5 (Testing every 5 days)

• contact_tracing_efficiency = 0.85 (85% contact tracing efficiency)

• enable_risk_communication = true
• risk_threshold = 25 (Intervention triggered with only 25 cases)

• awareness_increase = 0.15 (15% increase in awareness)

• behavior_change_rate = 0.08 (8% reduction in contacts)

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8.7 MSM-Focused Strategy
This strategy prioritizes the MSM population for interventions due to their higher risk, focusing on vaccina-
tion, testing, and risk communication within this group.

Agent Behavior: MSM agents have a 10% daily chance of vaccination (due to their higher risk and
the targeting of this intervention). They are also tested more frequently (every 4 days). If an MSM agent
tests positive, they and 95% of their contacts are quarantined. Risk communication is also targeted at MSM
agents, with awareness increasing by 15% and contact rates reducing by 7% when infections exceed 75.

• enable_vaccination = true
• vaccine_deployment_rate = 0.1 (10% of the MSM population vaccinated per day)
• enable_testing = true

• default_testing_frequency = 4 (Frequent testing for MSM)

• contact_tracing_efficiency = 0.95 (95% contact tracing efficiency among MSM)
• enable_risk_communication = true (Targeted risk communication for MSM)
• risk_threshold = 75

• awareness_increase = 0.15 (15% increase in awareness for MSM)

• behavior_change_rate = 0.07 (7% reduction in contacts for MSM)

25
9 Key Observations
Across all strategies, no outbreak was observed in the MSM population. This outcome is evident from the
infection curves, which ultimately declined to zero in every scenario.

Strategy 3, emphasizing risk communication, demonstrated a more rapid reduction in infections com-
pared to Strategy 1 (focused on vaccination) and Strategy 2 (focused on testing) under conditions of a
higher transmission rate (β). The faster containment can be attributed to the proactive dissemination of in-
formation, which likely influenced behavior changes and reduced transmission opportunities more effectively.

When combined interventions were implemented, the aggressiveness of the approach played a significant
role in mitigating the outbreak’s severity. For instance, Strategy 4, which employed aggressive deployment
of interventions, resulted in noticeably lower infection peaks compared to Strategy 5, which utilized a more
moderate approach. This highlights the importance of swift and robust implementation for optimal outcomes.

Finally, Strategy 6, characterized by early intervention, outperformed all other strategies. It not only
resulted in the lowest infection peaks but also ensured the fastest decline in the infection curve, effectively
curtailing the spread in the shortest possible time.

10 Conclusions
This research investigated the spread of monkeypox within a heavy-tailed sexual contact network represen-
tative of MSM populations, using an agent-based model. Our findings demonstrate the significant influence
of network heterogeneity and contact patterns on the outbreak’s trajectory. The results highlight the rapid
spread facilitated by highly connected individuals within the MSM network and the potential for spillover
into the broader community through household and workplace contacts. Varying the transmission probabil-
ity within the MSM network (µ) significantly impacted both the peak and timing of infections, especially
among MSM. Furthermore, even a small probability of workplace transmission accelerated the spread and
increased the overall outbreak size, emphasizing the importance of considering multiple transmission path-
ways. These insights emphasize the need for targeted public health strategies that account for the complex
interplay between network structure, contact patterns, and transmission probabilities to effectively control
monkeypox and similar diseases.

11 Extensions and Future Work

This research provides a foundation for further investigations into the dynamics of monkeypox and other
sexually transmitted infections within complex networks. Several extensions and future directions are worth
exploring:
1. Calibration with Real-World Data: Calibrating the model with detailed epidemiological data
from the 2022 outbreak or subsequent outbreaks would enhance its realism and predictive power. This
includes data on infection rates, contact tracing, and the effectiveness of interventions.
2. More Realistic Network Structures: Exploring more sophisticated network structures, incorpo-
rating degree assortativity, clustering, and temporal dynamics, would provide a more accurate rep-
resentation of real-world sexual contact patterns. This could involve using contact-tracing data or
network survey data to construct more realistic networks.

3. Impact of Interventions: Evaluating the effectiveness of different interventions, such as contact

tracking, ring vaccination, and public health campaigns promoting behavioral changes, would inform
public health policy and resource allocation. The model could be extended to incorporate the uptake
and effectiveness of these interventions.

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12 References

[1] Endo, A., et al. (2022). Heavy-tailed sexual contact networks and monkeypox epidemiology in the global
outbreak, 2022. Science, 378(6618), 90-94.
[2] Spicknall, I. H., et al. (2022). Modeling the Impact of Sexual Networks in the Transmission of Monkeypox
virus Among Gay, Bisexual, and Other Men Who Have Sex With Men – United States, 2022. MMWR
Morb Mortal Wkly Rep, 71(35), 1131-1134.
[3] Vivancos, R., et al. (2022). Community transmission of monkeypox in the United Kingdom, April to May
2022. Euro Surveill, 27(22), 2200422.
[4] Knight, J., and Tan, D.H.S. (2022). Maximizing the impact of limited vaccine supply under different
early epidemic conditions: a 2-city modelling analysis of monkeypox virus transmission among men who
have sex with men. CMAJ, 194(46), E1560-E1567.
[5] Cherian, P., Kshirsagar, J., Neekhra, B., Deshkar, G., Hayatnagarkar, H., Kapoor, K., Kaski, C., Kathar,
G., Khandekar, S., Mookherjee, S., Ninawe, P., Noronha, R.F., Ranka, P., Sinha, V., Vinod, T., Yadav, C.,
Gupta, D., & Menon, G.I. (2023). BharatSim: An agent-based modelling framework for India. medRxiv.
doi:10.1101/2023.06.15.23291292.

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