TemporalNetworkEpidemics

We provide methods from linear algebra to simulate infection processes on time-varying topologies. For more information see reference Koher, A. et a. Infections on Temporal Networks - A Matrix-Based Approach , PLoS ONE 11, 4, (2016)

Epidemics on temporal networks

The code implements three widely used epidemic models for simulation on temporal networks (ref [1]): SI, SIR and SIS. Each node can be either susceptible (S), infected (I) or recovered with permanent immunity (R). Furthermore, the disease transmission happens with a given probability upon contact and the recovery time is fixed to a number of time steps. The code comes with two data sets: A graph of sexual encounters and a face to face contacts network. The data has been downloaded from ref. [2] and ref. [3], respectively. More information on the approach that has been implemented here, can be found in ref [1] and following the link

[1] Koher, A. et al. "Infections on Temporal Networks - A Matrix-Based Approach" , PLoS ONE 11, 4, (2016)
[2] Rocha, L. et al., PLoS Comput Biol 7, 3, (2011).
[3] Stehlé J. et al., BMC medicine. 9(1), 87, (2011)

Susceptible - Infected - Recovered Model

We calculate the reachability for a SIR process as an example. A simulation with a SIS or SI model can be implemented accordingly. As an input, the algorithm takes a data set and the disease parameters, ie. the transmission probability and recovery time. As a result, one obtains a (boolean) reachability matrix, where each entry (ij) indicates a transmission path from node j to node i. This quantity is then used to derive the (mean) prevalence, incidence and cumulative incidence level.

Load packages

The main package EpiSim uses EpiMod, where the epidemiologicals are defined and readfile to load the data set.

%load_ext autoreload
%autoreload 2
from episim import EpiSim
import matplotlib.pyplot as plt
import numpy as np
import scipy.sparse as sp
%matplotlib inline

Run the simulation

episim_objekt = EpiSim(edgelist_fname="sociopatterns_hypertext.dat", #path/to/edgelist, Format: source,target,time,weight
                       directed=False, #Interpret edge list entries as undirected links (default)
                       observation_window=(None,None), #(int, int) Choose the first and last time step for the simulation.
                       aggregated=False) #Ignore time information to get a fully aggregated network. Default: False

episim_objekt.initialize()
episim_objekt.run_disease(model                 = "SIR", # Choose the model: "SIR", "SIS", or "SI"
                          recovery              = 3000,  # 1. disease parameter: recovery time
                          alpha                 = 1,     # 2. disease parameter: transmission probability
                          memory_efficient      = False, # Choose memory efficient (but slow) algorithm or large networks
                          track_single_outbreak = True,  # Save the incidence and prevalence levels for all nodes individually
                          save_matrix           = False, # Save the reachability matrix in (csr format)
                          verbose               = False) # Print output
episim_objekt.save(fname = "sociopatterns_SI")

Results

R = np.load("sociopatterns_SI.npz")
time = np.arange(R["runtime"])
plt.figure(figsize=(12,4))
plt.subplot(1,3,1)
for ii in range(nodes):
    plt.plot(time, R["single_prevalence"][ii,:] ,"k-",alpha=0.1, linewidth=.5)
plt.plot(time, R["mean_prevalence"],"-",alpha=1, linewidth=4)
plt.xlabel("time")
plt.ylabel("prevalence")

plt.subplot(1,3,2)
for ii in range(nodes):
    plt.plot(time, R["single_cumulative"][ii,:] ,"k-",alpha=0.1, linewidth=.5)
plt.plot(time, R["mean_cumulative"],"-",alpha=1, linewidth=4)
plt.xlabel("time")
plt.ylabel("cumulative incidence")

plt.subplot(1,3,3)
for ii in range(nodes):
    plt.plot(time, R["single_incidence"][ii,:]  ,"k-",alpha=0.2)
plt.plot(time, R["mean_incidence"],"-",alpha=1, linewidth=1)
plt.xlabel("time")
plt.ylabel("incidence")
plt.tight_layout()