Fast c++ implementation of simulations for nonlinear SIR model on networks

• A compiler with C++17 support
• python3
• if not already installed, pybind11 and setuptool will be installed in an isolated environment to build the package.

First, clone this repository. If using SSH (recommended)

git clone [email protected]:gstonge/fastsir.git

or

git clone https://github.com/gstonge/fastsir.git

Second, move to the directory of the project (cd /path/to/project/) then use pip to install the module.

pip install .

It is recommended to perform the installation in a virtual environment.

On the C++ side, we have a hierarchy of classes inheriting from the base (dummy) class

├── src
    ├── BaseContagion.hpp

Right now, there is only one derived class for discrete-time SIR models

├── src
    ├── DiscreteSIR.hpp

The C++ classes are "exposed" to python using pybind11.

├── src
    ├── bind.hpp

One should not have to deal with the C++ side, just import the class in python using

from fastsir import DiscreteSIR as sir

Everything revolves around the sir object (shorthand here for DiscreteSIR). To initialize the object, we need an edge list, a recovery probability for infected nodes, and a vector of infection probability. The latter gives the probability of getting infected per time step as a function of the infected degree, (number of infected nodes in the neighborhood).

Let's use the networkx package to get a graph

from fastsir import DiscreteSIR as sir
import numpy as np
import networkx as nx

#Network parameters
N = 10000
m = 10
p = 0.2
G = nx.watts_strogatz_graph(N,m,p)
max_degree = np.max([G.degree(n) for n in G])
edgelist = list(G.edges())

For the contagion process, we use some arbitrary parameter. For the infection probability, we assume a "simple contagion"

#contagion parameters
r = 0.01 #recovery probability
q = 0.0015 #from the demo on phase transition, we know this is close to criticality
recovery_probability = r
infection_func = lambda k: 1-(1-q)**k
infection_probability = infection_func(np.arange(max_degree+1))

Finally, or stochastic process is initialized like this

#initialize object
process = sir(edgelist,recovery_probability,infection_probability)

Now we need to infect a certain number of nodes initially at random. Here we use a single node, but more could be used. It must be a set.

initial_infected_nodes = {np.random.randint(N)}
process.infect_node_set(initial_infected_nodes)

Now to advance in time, we specify the period for which we want the process to evolve and call the method evolve:

period = 10
process.evolve(period,save_transmission_tree=True,save_macro_state=True)

Note: here we can specify if we want to keep track of the transmission tree and of the macro state (number of susceptible,infected,recovered) at each time. If we want to evolve until there are no more infected nodes---the process has died---, simply set period = np.inf.

After that, we can probe our process using various methods:

#get the current state of the network
S,I,R = process.get_current_macro_state()

#get the vector of macro state at each time step
macro_state_vector = process.get_macro_state_vector()

#get the transmission tree
tree = process.get_transmission_tree()

For more advanced usage, see the demos on transmission trees and phase transitions. Also, for a complete list of useful methods, do

help(sir)

or

help(process)