EoN Examples

We have collected a number of examples using EoN to generate figures. We start with examples from the book Mathematics of Epidemics on Networks: from Exact to Approximate Models. Then we give a few other examples. If none of these examples helps with the particular problem you are facing, Submit an issue or go to stackoverflow and use the ‘eon’ tag.

If you have an example you think would be useful here, please submit an issue or email me.

Reproducing figures from “Mathematics of Epidemics on Networks”

Here are examples to generate (close approximations to) many of the figures in Mathematics of Epidemics on Networks: from Exact to Approximate Models. Other examples are farther down.

Chapter 1

Introduction

• Figure 1.2
• Figure 1.5

Chapter 2

Top down models

• Figure 2.11

Chapter 3

Bottom up models

• Figure 3.2

Chapter 4

Homogeneous meanfield

• Figure 4.1
• Figure 4.5
• Figure 4.7
• Figure 4.8
• Figure 4.9
• Figure 4.10
• Figure 4.11
• Figure 4.12
• Figure 4.13

Chapter 5

Heterogeneous meanfield

For Chapter 5 figures, these examples use larger populations than the figures in the text.

Figures 5.3, 5.4, and 5.5 demonstrate the ease of the X_from_graph versions of the analytic equations

• Figure 5.2
• Figure 5.3
• Figure 5.4
• Figure 5.5

Chapter 6

Percolation and EBCM

The remainder of these simulations use reduced sizes or numbers of iterations compared to the published figure. This is to save time.

• Figure 6.1 (and 6.3)
• Figure 6.2
• Figure 6.3 is done in the same code as 6.1.
• Figure 6.4
• Figure 6.24

Chapter 7

Model hierarchies

• Figure 7.2
• Figure 7.3
• Figure 7.4

Chapter 9

Non-Markovian processes

For Chapter 9 (nonMarkovian) figures, we have not implemented code that solves the dynamic equations but we do have code that will do the simulations. These are given here.

• Figure 9.2
• Figure 9.4
• Figure 9.5

Additional Examples

Visualizing or animating disease spread

We can visualize snapshots or animations of disease spread in a network. For these examples, we’ll take a 100x100 grid of nodes [each node is (i,j)] connected to their 4 nearest neighbors (except the nodes on the edges). This isn’t the most realistic network, but it is a good example for showing the automatic plotting tools.

• Visualizing a snapshot of SIS disease spread in the network
• Visualizing an animation of SIR disease spread in the network
• Visualizing non-SIS/SIR processes (SIRV) spreading in the network

The last example shows how we might plot things like 'I'+'R' or other combinations of the data.

Non-uniform infectiousness

Perhaps the population is made up of different types of individuals with different infectiousness. This example considers a heterosexual population where one group is more infectious than the other. This example includes a user-defined transmission function and uses the simulation investigation tools to look at the dynamics in each population.

• Bipartite population

Weighted networks

You may have edges (or nodes) with weights affecting transmission or recovery rates. (for this be aware that the syntax of edge/node attributes is different for networkx 2.x and 1.x).

• SIS weighted edges

Non-SIS/SIR processes with Gillespie_simple_contagion

The default Gillespie and Event-driven algorithms assume SIS or SIR dynamics. However, you may want something else, such as SEIR or SIRS or maybe more exotic things. If you are willing to assume that events all happen as Poisson processes (that is, an event happens at a rate), then it’s possible to do this with a Gillespie approach.

Note that right now if a node has an edge to itself, this can cause the code to crash. I will try to fix this soon.

• SEIR (with simple heterogeneities)
• SEIRT (SEIR + tracing)
• SIRS
• SIRS (with more complicated heterogeneity)
• Competing SIR Diseases
• Cooperative SIR Diseases
• SIR with random concurrent vaccination

Other

Are you trying to do something but can’t figure it out and would like an example?

Submit an issue or go to stackoverflow and use the ‘eon’ tag. I’ll try to help.

If you have developed something that you think would make a good example and you’d like to share it, please let me know.