Simulate Evolution of Graphs

The Notebook Below Simulates an Evolving Graph based on the Susceptible-Infected Susceptible model

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The code produces trajectories in terms of the fraction of the infected population :math:` heta_I` and the fraction of the edges between the susceptible population $g_{ss} $

References:

• Gross, Thilo, and Ioannis G. Kevrekidis. “Robust oscillations in SIS epidemics on adaptive networks: Coarse graining by automated moment closure.” EPL (Europhysics Letters) 82.3 (2008): 38004.

• Kattis, Assimakis A., et al. “Modeling epidemics on adaptively evolving networks: a data-mining perspective.” Virulence 7.2 (2016): 153-162.

Dependencies

• numpy pip install numpy

• matplotlib pip install matplotlib

• tqdm pip install tqdm

One sampled trajectory for \(p=0.00075\) from the evolving graph is shown in the figure below

Trajectory_display.png

import numpy as np
import matplotlib.pyplot as plt
from tqdm.notebook import tqdm
from Full_Network_Functions import * ##

plt.rc('xtick', labelsize=20)
plt.rc('ytick', labelsize=20)
plt.rc('axes', labelsize=21)
plt.rc('font', family='serif')
plt.rc('font', family='serif')
plt.rcParams['image.cmap'] = 'Spectral'
np.random.seed(2)

Parameters Used For The Simulation Below

The Parameters governing: * The number of Nodes, \(N=10,000\) * The number of Edges, \(L=100,000\) * The inital fraction of Infected people, \(Y_0 =0.5\) are kept fixed on the Full_Network_Functions.py file.

w0 = 0.06 #rewiring parameter
r = 0.0002 #recover probability
p = 0.00075 #infection parameter

Load an initial configuration of the graph

The user can choose between initializing a random graph or loading an existing graph

data = load_initial_graph_question()

Do you want to load an existing graph? (yes or no)yes

Run Simulations for the graph

For \(p=0.00075\) you might need to run about 20,000 steps (~20 mins) to capture the stable limit cycle

Number_of_Steps=int(input('Select the Number of Time Steps:' ))
stat_list = []
I_node = data[0];edge_list = data[1]
stat_array, I_node, edge_list = iterate(I_node, edge_list, Number_of_Steps,r, p,w0)

Select the Number of Time Steps:100

100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:07<00:00, 12.93it/s]

fig = plt.figure(figsize=(4*3,4))
ax = fig.add_subplot(131)
ax.plot(stat_array[:,0],'.k')
ax.set_ylabel(r'$   heta_I$')
ax.set_xlabel('Iterations')

ax = fig.add_subplot(132)
ax.plot(stat_array[:,1],'.k')
ax.set_ylabel(r'$g_{ss}$')
ax.set_xlabel('Iterations')

ax = fig.add_subplot(133)
ax.plot(stat_array[:,0],stat_array[:,1],'.k')
ax.set_ylabel(r'$g_{ss}$')
ax.set_xlabel(r'$   heta_I$')

plt.tight_layout()