# Epidemic Spreading in Urban Areas Using Agent-Based Transportation Models

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## Abstract

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## 1. Introduction

- Using a large-scale agent-based transport simulation model, it is feasible to describe individual behavior throughout an epidemic outbreak. Not only can the locations, the person-to-person interaction time, and the activities of each individual be simulated, but also the interactions between household members and their behavior changes can be taken into account.
- Because each person is represented individually, it is possible to directly assign infection and recovery probabilities to them, which provides a more realistic representation than the parameter-based approach of classical epidemic spread models.
- The proposed approach allows the recreation of historical events of epidemic outbreaks. Using the metropolitan area of Zurich, Switzerland, it is shown that even with simple assumptions the agent-based model gives a good approximation of the seasonal influenza outbreak observed in 2016/2017.

## 2. Background

#### 2.1. Classical Epidemic Spread Models

#### 2.2. Complex Network Epidemic Spread Models

#### 2.3. Agent-Based Epidemic Spread Models

## 3. Methods

#### 3.1. Generic Epidemic Spread Model

- A constant and closed population is assumed meaning that although the number of individuals in each disease state changes over time, the sum of all states is always equal to the population size. Demographic turnovers and fatalities due to the virus are not considered.
- Every agent has the same probability ${\mathbb{P}}_{\beta}$ to get infected, even though children are much more infectious than adults and shed virus from just before they develop symptoms until two weeks after infection. Additionally, every susceptible agent in a facility has the probability of getting infected, even if there is no direct contact with an infected agent.
- It is assumed that infected agents do not change their daily activities, i.e., they continue with their original plans.
- Every agent has the same probability ${\mathbb{P}}_{\gamma}$ of getting recovered.

#### 3.2. Agent-Based Model

#### 3.3. Model Calibration and Validation

- Defining the agents in terms of basic socio-demographic data and home location
- Assigning an activity schedule to each of these agents.

#### 3.4. Implementation

**Numerical study**: The first example is a numerical study where a series of simulations are performed with varying input parameters ${\mathbb{P}}_{\beta}$, ${\mathbb{P}}_{\gamma}$ and ${\mathbb{P}}_{I}$. The aim is to test the variability of the model and to investigate the sensitivity of the individual parameters. Furthermore, it serves as a basis for the second example and the identification of further research priorities.**Historical event**: While the first example gives a general insight into the model, this example aims at the best possible reproduction of a historical event with the gained knowledge. To achieve this, the agent-based epidemic spread model and the classical compartment SIR model are fitted to real data of seasonal influenza in the season 2016/2017 observed in the Zurich area [35].

## 4. Result and Discussion

#### 4.1. Numerical Study

#### 4.1.1. Temporal-Spatial Resolution

#### 4.1.2. Varying Parameters

#### 4.2. Historical Event

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

S | Susceptible |

I | Infected |

R | Recoveredthree |

MATSim | Multi-Agent Transport Simulation |

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**Figure 1.**Scheme of the basic SIR model. Boxes represent compartments, and arrows indicate flux between the compartments.

**Figure 2.**Schematic representation of a metapopulation model. The system is composed of a heterogeneous network of subpopulations or patches, connected by migration processes. Each patch contains a population of individuals who are characterized with respect to their stage of the disease (e.g., susceptible, infected, removed), and identified with a different color in the picture. Individuals can move from a subpopulation to another on the network of connections among subpopulations. (Taken from Colizza and Vespignani [25]).

**Figure 3.**Scheme of the generic epidemic spread model. Each agent can be assigned to a disease state (S, I, R). If a susceptible agent is in contact with an infected agent, with (transition) probability ${\mathbb{P}}_{\beta}$, the agent becomes infected. At the end of the day each infected agent has a (transition) probability ${\mathbb{P}}_{\gamma}$ to recover.

**Figure 7.**Some of the simulation results from the SIR model with varying input parameters ${\mathbb{P}}_{I}$, ${\mathbb{P}}_{\beta}$ and ${\mathbb{P}}_{\gamma}$. With: (

**a**) reference scenario, (

**b**) increased initially infected population, (

**c**) increased infection probability, (

**d**) decreased recovery probability, (

**e**) increased recovery probability, and (

**f**) decreased infection and recovery probabilities.

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Hackl, J.; Dubernet, T.
Epidemic Spreading in Urban Areas Using Agent-Based Transportation Models. *Future Internet* **2019**, *11*, 92.
https://doi.org/10.3390/fi11040092

**AMA Style**

Hackl J, Dubernet T.
Epidemic Spreading in Urban Areas Using Agent-Based Transportation Models. *Future Internet*. 2019; 11(4):92.
https://doi.org/10.3390/fi11040092

**Chicago/Turabian Style**

Hackl, Jürgen, and Thibaut Dubernet.
2019. "Epidemic Spreading in Urban Areas Using Agent-Based Transportation Models" *Future Internet* 11, no. 4: 92.
https://doi.org/10.3390/fi11040092