Agent-Based Epidemiological Simulation

This project aims to determine and quantify the effects of implementing lockdown, mass testing, quarantine delays, and social distancing in controlling the spread of a disease. In particular, we focus on the effects of these interventions to the recovery and death rates. In this article, we will focused first on discussing the approach we took to model a simple epidemiological simulation using a technique known as agent-based modelling. This article will also discuss the tools used, as well as instructions on how to explore our model yourselves. A separate article will be dedicated to performing analysis on the simulation results.

What is Agent-Based Modelling?

Agent-based modelling (ABM) is a technique that models a complex system by reducing it to the interactions between agents and their environment. Here, agents can possess properties such as age and gender, and can perform actions based on pre-defined set of conditions. The environment possesses properties as well, and can affect the behavior of agents and vice versa. Observables such as population growth can then be measured to infer relationships between agent behavior and the overall behavior of the system. This makes ABMs powerful in that it can be used to observe and quantify the macroscopic behavior of many complex systems over time just by knowing how individual agents behave. This can be achieved without the need to construct differential equations that requires pre-existing knowledge of the relationships between observables.

Currently, there are a number of platforms that provide users with tools needed to build an ABM simulation. For this project, we’ll be using Netlogo.

Netlogo is an open source, cross-platform multi-agent programmable modeling environment. Its user-friendly language allows users to quickly draft prototypes and visualize the results through an interactive customizable interface. In addition, Netlogo also includes dozens of pre-built models ranging from tumor growth simulation, to modelling behavior of gas particles. For more information, visit the official Netlogo site: https://ccl.northwestern.edu/netlogo/.

Getting Started

To begin, you need to download the latest version of Netlogo using the following link: https://ccl.northwestern.edu/netlogo/download.shtml. When unpacked, a folder containing all the necessary files will be created. Open the Netlogo application file to launch.

Clone Repository

Next, go to our repository using the link: https://github.com/magoanalytics/agent-based-epidemiological-simulation. After cloning the repository, load epi_model.nlogo from the file tab. Alternatively, you can simply double-click epi_model.nlogo from the repository folder.

Setup and Go Procedures

Move the sliders and/or select values from the drop-down list in the interface tab to modify hyperparameters to their desired values, then click Setup button to initiate and update changes to the model. Click Go button to run the simulation. A chart plotting the variables of interest, such as the number of infected and recovered agents, are shown on the left side of the interface. On the right side, a view of the simulation is updated at each tick. For a complete list of hyperparameters, refer to the Model Parameters section.

sample_setup

Modelling Approach

To model the spread of the disease in a population, we need to properly define the rules that govern how each agent behaves, as well as the interactions between the agents and its environment. In addition, agent behavior will have to be defined separately for simulations that include interventions. This section aims to explain our approach in detail.

Agent Behavior

Agents are allowed to move around the world, infect other agents, recover, or die from the disease depending on the its current properties and surrounding environment. Agents can either be in the following states: susceptible, infected, recovered, or dead. To differentiate one state from the other, agents that are susceptible, infected, or recovered are colored green, red, and blue, respectively. The exception would be when an agent is considered dead, in which case the agent is removed from the simulation entirely.

At each tick, here defined to be an hour, agents are allowed to move in a random direction. If a susceptible agent is near an infected agent, the latter has a probability of being infected equal to its vulnerability. Here, vulnerability is an agent-level parameter that is used to model a person’s hygiene, where a higher vulnerability value corresponds to lower hygenic behavior. On the other hand, if an infected agent has been sick for more than or equal to its recovery-time, it has a probability of recovering equal to its recovery-rate. However, at each tick, an infected agent also has a probability of dying equal to its death-rate.

It is assumed that agents that have recovered gain full immunity, and therefore cannot be infected twice.

Environment

The environment is where the simulation takes place. This is composed of an NxN grid boxes of equal area called patches. Each patch can either be a normal patch, border patch, or a quarantine patch. To differentiate these patches, the border patches are colored dark yellow while quarantine patches are colored light yellow. Normal patches are colored black.

Border patches divide the environment into areas that can represent a town or even an entire city. Quarantine patches can be found at the center. Infected agents that are quarantined are not allowed to leave the area in order to prevent them from further spreading the disease.

For completeness, it is worth noting that the environment is modelled to be bounded, or where wrapping is not allowed. This prevents agents from travelling from the edge of the world to the other edge of the world instantaneously.

Next, we discussed the interventions included in the model.

Lockdown

During lockdowns, agents have a probability of crossing border patches equal to the lockdown-intensity value. This allows us to simulate not only complete lockdowns, but also those that are partially implemented.

Quarantine and Isolation

Every 24 ticks, each agent has a probability of being test equal to the mass-testing-intensity value. This allows us to simulate mass testing, where everyone is tested regardless of whether the person is showing symptoms or not, as well as simulating testing done on a much smaller scale. To simulate the delay between a person being tested positve to when the person is quarantined, an additional parameter is added named quarantine-delay, which ranges from one day to up to one week. An agent that is quarantined is transferred to an isolated area in order to prevent the agent from infecting other agents.

Social Distancing

To quantify the effects of distancing oneself from other people, the parameter named social-distancing-intensity is added. Each agent has a probability of maintaining a fixed distance from the agent nearest to it equal to the value of this paramter. This allows us to simulate the behavior of the entire system for cases where everyone complies with social distancing and where only a portion of people do.

Model Parameters

To determine their effects, a set of parameters is assigned to each intervention. These parameters can be turned “on” or “off” by setting them to higher or lower values to increase or decrease their effects, respectively. For example, to isolate the effectiveness of lockdown, one can increase the lockdown-intensity factor while setting the parameters mass-testing-intensity and social-distancing-intensity to 0. The overall effectivess of combined interventions can also be explored by adjusting the appropriate parameters. The table below lists the hyperparameters, together with a short description and possible values, that can be adjusted in the interface tab:

Model Parameter Description Value
initial-population Initial number of agents at the start of the simulation (t = t0) [10,5000]
initial-infected Initial number of infected agents at the start of the simulation (t = t0) [1, 10]
average-vulnerability Average probability of a person being infected when near infected agent(s) [0, 100]
average-recovery-rate Average probability of an infected agent to recover [0, 100]
average-recovery-time Average time needed for an agent to have a chance to recover after being infected {336, 504, 672}
average-death-rate Average probability of an infected agent dying [0, 1]
lockdown-intensity Average probability of an agent attempting to cross border to cross successfully [0, 100]
mass-testing-intensity Probability of an agent being tested every 24 hours [0, 100]
quarantine-delay Number of days before infected agent is quarantined after being tested positve [1, 7]
social-distancing-intensity Probability of an agent to observe social distancing [0, 100]


Next Steps

Now that we have a better understanding of the modelling approach, we can proceed to perform simulation runs and do analysis. On our next article, we’ll be focusing on analyzing and quantifying the effects of the above mentioned interventions to the infection, recovery, and death rates.

Project By