26. Basic agent-based modeling

Section author: Almond Heil <almondheil@gmail.com>

26.1. Motivation, Prerequisites, and Plan

In this chapter, we will learn the basics of agent-based modeling by creating and customizing a simple model using the Mesa framework. While following along, you should keep in mind that the Mesa framework is one of many ways to approach agent-based modeling in Python.

An agent-based model takes a bottom-up approach to solving a problem, by considering the smallest indiviual members (or agents) that make up a larger system and examining how they interact with each other.

Before you start, make sure you fulfill the following prerequisites.

  • The 10-hour “serious programming” course

  • This program will have heavy dependencies, so we will use a python virtual environment:

    $ sudo apt install python3-venv
    $ python3 -m venv mesa-venv/
    $ source mesa-venv/bin/activate
    
  • Installing the required packages with pip.

    $ # (now you should have a prompt indicating you are in the vent)
    $ pip3 install mesa solara altair
    $ pip3 install networkx matplotlib
    

Now that you’re ready, here’s what we’ll be doing in today’s course!

  1. Learn about the basics of agent-based modeling and object-oriented programming

  2. Create the classes for a simple infection model

  3. Place agents in space and move them

  4. Create a visualization of the model

  5. Manage infection spread among agents

  6. Gather and plot data

26.2. Conceptualizing the model

When building an agent-based model, it’s important to consider the basic building blocks that will make up our model. Based on the broad idea of how diseases spread, we will narrow our focus to how diseases spread by direct contact.

To understand our model as it develops, it’s important to understand a few terms, both from agent-based modeling and object-oriented programming. Some short definitions appear below.

26.2.1. Agent-Based Modeling Concepts

model

An abstraction of reality seeking to distill the behaviors of a complex system so we can understand it more easily.

In Mesa, the model is specifically the structure that manages setting up and running your program, including the agents inside of it.

agent

One of the entities within an agent-based model (wow, what a circular definition!) It can interact with other agents and the world in various ways.

step

A single unit of time in the model. Can also refer to a method an agent follows every time unit.

26.2.2. Object-Oriented Programming Concepts

class

An object-oriented programming concept which refers to a structure containing the framework for making objects–what they can do, what data they hold, etc.

object

One instance of a class, which inherets the structure that’s been set up for it. We’ll take advantage of this to create many agent objects based on a single class.

method

A function that belongs to a class, and can be called by any object based on that class. For instance, we might expect each agent to be able to move around with an agent.move() method.

26.3. Classes and steps

To implement these concepts, we’ll create a model. Create a file called direct_contact_step1.py and enter this code.

Listing 26.3.1 direct_contact_step1.py
#! /usr/bin/env python3

from mesa import Agent, Model

class InfectionAgent(Agent):
    def __init__(self, model, infected):
        super().__init__(model)
        self.infected = infected

    def step(self):
        print(f"agent {self.unique_id}; infected {self.infected}")


class InfectionModel(Model):
    def __init__(self, N, seed=None):
        super().__init__(seed=seed)
        self.num_agents = N

        for i in range(self.num_agents):
            a = InfectionAgent(self, False)
            self.agents.add(a)

    def step(self):
        self.agents.shuffle_do('step')

Above, we define two classes. InfectionAgent is based on Mesa’s agent class, and we define how it acts when it initializes and when it steps. By using super().__init__(model) in the InfectionAgent’s intialization code, we tell it to set up state common to all agents (for example, a unique ID). We also set the agent’s infected status to false, which we’ll edit down the line to start an infection.

InfectionModel is based on Mesa’s model class. When it initializes, it creates a schedule to run the model with and adds agents to it, passing them the model parameter.

Now, it’s time to see the code in action! In your terminal, open a live Python session by typing python3 and enter the following.

>>> from direct_contact_step1 import *
>>> model = InfectionModel(10)
>>> model.step()

You will see the program output something like this.

agent: 1 infection: False
agent: 5 infection: False
agent: 9 infection: False
agent: 8 infection: False
agent: 4 infection: False
agent: 3 infection: False
agent: 7 infection: False
agent: 2 infection: False
agent: 6 infection: False
agent: 0 infection: False

If you repeat model.step(), you will notice that the order the agents call out is different each time. This is because of the call to self.agents.shuffle_do('step') in the model’s step() method.

Note

When you want to test changes you’ve made to your model, make sure to exit your python interpreter with Control+D or by typing exit(). Then, start a new session and import the code again to see your most recent changes take effect.

26.4. Space and movement

Now that each agent is able to take steps, we will add space and movement to our model. For this example we will be using a grid for simplicity, as well as Mesa’s built-in support for grid visualization.

To keep everything straight you might want to copy the file direct_contact_step1.py to a new filename, like direct_contact_step2.py with:

$ cp direct_contact_step1.py direct_contact_step2.py

and we will edit and make modifications to direct_contac_step2.py

First, we import the necessary components to our project. In this case we want to use a MultiGrid, so that multiple agents can be on top of each other in the same grid cell.

Listing 26.4.1 direct_contact_step2.py - add spacial information
from mesa.space import MultiGrid

Then, we can edit out model’s __init__ method to let it take width and height parameters. We also change our method of placing agents to give them random positions using the model’s random number generator. This generator functions just like the normal Python random module, but it allows us to easily set seeds if we want to reproduce our results down the line.

Listing 26.4.2 direct_contact_step2.py - the InfectionModel
class InfectionModel(Model):
    def __init__(self, N, width, height, seed=None):
        super().__init__(seed=seed)
        self.num_agents = N
        self.grid = MultiGrid(width, height, torus=True)

        for i in range(self.num_agents):
            a = InfectionAgent(self)
            x = self.random.randrange(self.grid.width)
            y = self.random.randrange(self.grid.height)
            self.grid.place_agent(a, (x, y))
            self.agents.add(a)

The third argument of MultiGrid represents whether the space is toroidal, meaning that agents who walk of one edge of the grid will reappear on the other side. This emulates an infinite space, and helps us avoid issues with agents hiding in corners or being trapped and unable to move.

To add movement, we need to change what happens when an agent takes a step. First, add the move method, which tells the agent to move to a random cell near itself:

Listing 26.4.3 direct_conract_step2.py - the InfectionAgent
def move(self):
    x, y = self.pos
    x_offset = self.random.randint(-1, 1)
    y_offset = self.random.randint(-1, 1)
    new_position = (x + x_offset, y + y_offset)
    self.model.grid.move_agent(self, new_position)

Now we’ve defined how the agent moves, but we have not yet told it to do that when step() gets called. Go ahead and add the instruction to move, and also update the print statement to tell us the agent’s position – right now nothing’s going to show up onscreen.

Listing 26.4.4 direct_contact_step2.py - the InfectionAgent step() function
def step(self):
    self.move()
    print(f"agent {self.unique_id}; pos {self.pos}; infected {self.infected}")

Now, try running the code again–with one difference. Now that the model takes parameters for its width and height, we need to provide those when we create it like so.

>>> from direct_contact_step2 import *
>>> model = InfectionModel(10, 30, 20)
>>> model.step()

If you’re having any issues, go ahead and check your work so far against this example. You can do so using diff -u in the command line. Of course, I’m not going to stop you from copy-pasting this working example, but c’mon.

Listing 26.4.5 direct_contact_step2.py
#!/usr/bin/env python3

from mesa import Agent, Model
from mesa.space import MultiGrid

class InfectionAgent(Agent):
    def __init__(self, model):
        super().__init__(model)
        self.infected = False

    def move(self):
        x, y = self.pos
        x_offset = self.random.randint(-1, 1)
        y_offset = self.random.randint(-1, 1)
        new_position = (x + x_offset, y + y_offset)
        self.model.grid.move_agent(self, new_position)

    def step(self):
        self.move()
        print(f"agent {self.unique_id}; pos {self.pos}; infected {self.infected}")

class InfectionModel(Model):
    def __init__(self, N, width, height, seed=None):
        super().__init__(seed=seed)
        self.num_agents = N
        self.grid = MultiGrid(width, height, torus=True)

        for i in range(self.num_agents):
            a = InfectionAgent(self)
            x = self.random.randrange(self.grid.width)
            y = self.random.randrange(self.grid.height)
            self.grid.place_agent(a, (x, y))
            self.agents.add(a)

    def step(self):
        self.agents.shuffle_do('step')

26.5. Visualization

Now we are able to move the agents, but we have no idea of where they are going. Of course, you could add the print statement back in, but with the constant movement and random schedule order it becomes difficult to keep track of what’s going on. To make this easier, we want to add visualization.

Before we make changes let us copy to a new filename, this time from direct_contact_step2.py to direct_contact_step3.py

$ cp direct_contact_step2.py direct_contact_step3.py

You can right away add this line to the import statements at the top:

from mesa.datacollection import DataCollector

We then need to add one instruction to our main direct_contact_step3.py file. In the init method for InfectionModel, add the line self.running = True and a line to initialize a “data collector”. It should now match the code below:

Listing 26.5.1 direct_contact_step3.py - the InfectionModel __init__()
def __init__(self, N, width, height, seed=None):
     super().__init__(seed=seed)
     self.num_agents = N
     self.grid = MultiGrid(width, height, torus=True)
     self.running = True
     self.datacollector = DataCollector(
         model_reporters = {"Infected": compute_infected})

Now, we need to create a visualizer which will display our model and let us interact with it. In this case, we’ll be using Mesa’s built-in visualization tools because they’re accessible and work well for our purposes. Create a new file called visualization_step3.py and add the following to it.

Listing 26.5.2 visualization_step3.py
#!/usr/bin/python3

from mesa.visualization import SolaraViz, make_plot_component, make_space_component

# change this to match your file name if it's not direct_contact_step3.py!
from direct_contact_step3 import *

# The parameters we run the model with.
# Feel free to change these!
model_params = {"N": 30,
                "width": 15,
                "height": 10}

def agent_portrayal(agent):
    portrayal = {"Shape": "circle",
                 "color": "grey",
                 "Filled": "true",
                 "Layer": 0,
                 "r": 0.75}
    if agent.infected:
        portrayal["color"] = "LimeGreen"
        portrayal["Layer"] = 1
    return portrayal

infection_model = InfectionModel(model_params["N"],
                                 model_params["width"],
                                 model_params["height"])
SpaceGraph = make_space_component(agent_portrayal)
InfectedPlot = make_plot_component("Infected")

page = SolaraViz(infection_model,
                 model_params=model_params,
                 components=[SpaceGraph, InfectedPlot],
                 name="Infection Agent visualization")

# if you are using a jupyter notebook then you should uncomment this line that
# just says "page"; otherwise you need to run the program with "solara run
# visualization_step3.py"

# page

There’s a lot to unpack in this block of code, because a lot is going on under the hood with Mesa’s modules. First, we create a dictionary called params. It holds the names and values for each parameter the model takes in its __init__. Under the hood, Mesa is unpacking this dictionary to use the values as keyword arguments or kwargs, which are used in "name": value pairs to initialize the model.

Next, we define the function agent_portrayal. It takes an individual agent from the model as input, and outputs the necessary information to draw the agents. Mesa takes care of its visualization with a web browser window, which handles graphics and user interaction with JavaScript.

Luckily, we don’t have to deal with the JavaScript side of the equation because Mesa’s SolaraViz module takes care of it - all you will notice is a new tab in your browser pop up. We only need to pass it the portrayal method to use, the dimensions of the grid, and the pixel size of the grid to be displayed.

We then create the infection model, and we also create visual panels called SpaceGraph and InfectedPlot which you will see when you run this file.

Finally, we create the visualizer which makes a visualization web page with this line:

Listing 26.5.3 visualization_step3.py - the actual call to make the plot page
page = SolaraViz(infection_model,
                 model_params=model_params,
                 components=[SpaceGraph, InfectedPlot],
                 name="Infection Agent visualization")

This will define the web server. It unites several data structures we’ve already created. The first term infection_model is the model to use. The second has the parameters to run the model with. The third holds a list of the display methods to use (such as the grid we just defined and the plot of how many are infected). The fourth is simply the title to display.

See also

The mesa visualization, as of version 3 of mesa, uses the Solara framework to draw graphics into a web browser window. More information is available at: https://solara.dev/

With all this done, we can run the model with a single command from the terminal!

$ solara run visualization_step3.py

Once the server has started it will open a browser window and you can click the “Start” button in the top right to run your model, or the “Step” button move forward incrementaly.

With the server running, you will see a display like this. At this point, you’ll only see the agents wandering around, but we’ll have them spread infection to each other in the next step.

Grid with several grey agents populating it.

Figure 26.5.1 Grid with several grey agents populating it and just one infected green one.

Note

The server won’t automatically quit when you click “Stop” or close the browser tab that is displaying it. To stop the model fully, you have to go to the terminal running the model and press Control+C.

26.6. Interactions between agents

Until now our agents have moved around, and occasionally jostled each other, but they have not yet passed the infection on.

We now add a method for the InfectionAgent class that allows agents to infect each other. In this method, we use Mesa’s built-in get_neighbors method to collect a list of all the agents next to a given point. The parameters “moore” and “include_center” specify what counts as a neighboring space. Moore means that diagonal spaces are included, and include_center counts the space that an agent is on.

Start by copying the _step3.py files to _step4.py:

$ cp direct_contact_step3.py direct_contact_step4.py
$ cp visualization_step3.py visualization_step4.py

Quickly edit visualization_step4.py to have:

Listing 26.6.1 visualization_step4.py - change to import direct_contact_step4
from direct_contact_step4 import *

But most of our work will be in the direct_contact_step4.py file where we will adjust the agent model to be infectuous.

Listing 26.6.2 direct_contact_step4.py - the InfectionAgent infect_neighbors() method
def infect_neighbors(self):
    neighbors = self.model.grid.get_neighbors(self.pos,
                                              moore=True,
                                              include_center=True)
    for neighbor in neighbors:
        if self.random.random() < 0.25:
            neighbor.infected = True

Next, we’ll edit the agent step method to infect any neighbors only if it is infected.

Listing 26.6.3 direct_contact.py - InfectionAgent: add the call to infect_neighbors()
def step(self):
    self.move()
    if self.infected:
        self.infect_neighbors()
    print(f"agent {self.unique_id}; pos {self.pos}; infected {self.infected}")
Exercise 26.1: Routes of infection

As you’ll notice, we take an extremely simple aproach to infection: For each of our direct neighbors, we have a 25% chance of infecting them.

What other ways might this disease spread (for instance, only by touch when we stood on the same grid cell as another person)? How might you change the code to reflect these differences?

To support the visualization in visualization_step4.py you should introduce a call to datacollector.collect() in the model’s step() method. This will be called by the visualization system to get information for making its plots.

Listing 26.6.4 direct_contact.py - InfectionModel: add the collect() call to the step() method
 def step(self):
     self.agents.shuffle_do('step')
     self.datacollector.collect(self)

To support visualization you also need to define that compute_infected() method. Put this near the top of direct_contact_step4.py, just after the import statements, and just before the definition of the classes.

Listing 26.6.5 direct_contact.py - define the compute_infected() function
def compute_infected(model):
    infected = 0
    for agent in model.agents:
        if agent.infected:
            infected += 1
    return infected

Run it with:

$ solara run visualization_step4.py

When you run the model now, it will look something like this. This screenshot was taken after some 13 steps, and the infection has spread to a bit less than half the population.

Grid populated with agents, some normal and some infected.

Figure 26.6.1 Grid populated with agents, some normal and some infected.

If something isn’t running properly, we give you both programs below:

Listing 26.6.6 direct_contact_step4.py
#!/usr/bin/env python3

from mesa import Agent, Model
from mesa.space import MultiGrid
from mesa.datacollection import DataCollector

def compute_infected(model):
    infected = 0
    for agent in model.agents:
        if agent.infected:
            infected += 1
    return infected

class InfectionAgent(Agent):
    def __init__(self, model, infected):
        super().__init__(model)
        self.infected = infected

    def move(self):
        x, y = self.pos
        x_offset = self.random.randint(-1, 1)
        y_offset = self.random.randint(-1, 1)
        new_position = (x + x_offset, y + y_offset)
        self.model.grid.move_agent(self, new_position)

    def infect_neighbors(self):
        neighbors = self.model.grid.get_neighbors(self.pos,
                                                  moore=True,
                                                  include_center=True)
        for neighbor in neighbors:
            if self.random.random() < 0.25:
                neighbor.infected = True

    def step(self):
        self.move()
        if self.infected:
            self.infect_neighbors()
        print(f"agent {self.unique_id}; pos {self.pos}; infected {self.infected}")

class InfectionModel(Model):
    def __init__(self, N, width, height, seed=None):
        super().__init__(seed=seed)
        self.num_agents = N
        self.grid = MultiGrid(width, height, torus=True)
        self.running = True
        self.datacollector = DataCollector(
            model_reporters = {"Infected": compute_infected})
        
        for i in range(self.num_agents):
            infected = True if i == 0 else False # infect just the 0th agent
            a = InfectionAgent(self, infected)
            x = self.random.randrange(self.grid.width)
            y = self.random.randrange(self.grid.height)
            self.grid.place_agent(a, (x, y))

    def step(self):
        self.agents.shuffle_do('step')
        self.datacollector.collect(self)
Listing 26.6.7 visualization_step4.py
#!/usr/bin/python3

from mesa.visualization import SolaraViz, make_plot_component, make_space_component

# change this to match your file name if it's not direct_contact_step3.py!
from direct_contact_step4 import *

# The parameters we run the model with.
# Feel free to change these!
model_params = {'N': 30,
                'width': 15,
                'height': 10}

def agent_portrayal(agent):
    portrayal = {'Shape': 'circle',
                 'color': 'grey',
                 'Filled': 'true',
                 'Layer': 0,
                 'r': 0.75}
    if agent.infected:
        portrayal['color'] = 'LimeGreen'
        portrayal['Layer'] = 1
    return portrayal

infection_model = InfectionModel(model_params['N'],
                                 model_params['width'],
                                 model_params['height'])
SpaceGraph = make_space_component(agent_portrayal)
InfectedPlot = make_plot_component('Infected')

page = SolaraViz(infection_model,
                 model_params=model_params,
                 components=[SpaceGraph, InfectedPlot],
                 name='Infection Agent visualization')

# if you are using a jupyter notebook then you should uncomment this line that
# just says "page"; otherwise you need to run the program with "solara run
# visualization_step3.py"

# page

We conclude by showing the final state, in which the entire population has been infected:

Grid populated with agents, all of them infected.

Figure 26.6.2 Grid populated with agents, all of them infected.

This simplistic model of infection might be compared to a “zombie apocalypse”: nobody recovers or dies, and eventually the entire population has been infected.

26.7. The final source code

Here are the completed versions of the two final files we produced.

direct_contact.py

visualization.py

We have removed the _step4 so you can now simply run with:

$ solara run visualization.py

to have the code run and visualize in your browser.

26.8. Making an SIR model

Here are files with a partial implementation of an SIR model based on the simple infection model above.

Download these files:

sir_model.py

sir_vis.py

Remember to run:

$ python3 sir_vis.py

to have the code run and visualize in your browser.

The model seems to work and to show the behaviors you see when you solve the SIR differential equations. After 120 steps we see some oscillation in the S, I, R values:

SIR model after 120 stepse.

Figure 26.8.1 SIR model after 120 steps.

And after 360 setps you see a few more oscillations:

SIR model after 360 stepse.

Figure 26.8.2 SIR model after 360 steps.

26.9. Further reading

You’ve completed this course, but there’s more to look into in this book and elsewhere if you’re interested in agent-based modeling and how agents behave together! Feel free to check out some of the resources below.

Exercise 26.1: A real SIR model!

If you feel up to it, see if you can build on the model we made here to make an actual SIR model, where agents only stay infected for a limited amount of time before being removed from the population (or recovered, if you want to put a positive spin on it.)

There are some ordinary differential equations behind SIR models, so based on your mathematical experience you might feel more or less comfortable dealing with them (I’ll admit, they definitely can be scary).

If you’re looking for a place to start, try adding a way for agents to become no longer infected by the disease, and see what questions and problems stem off of that.

You could use the examples above in the files sir_model.py and sir_vis.py as a starting point.