NetSIRSF.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat May 11 08:56:41 2019

@author: nolte

D. D. Nolte, Introduction to Modern Dynamics: Chaos, Networks, Space and Time, 2nd ed. (Oxford,2019)
"""

# https://www.python-course.eu/networkx.php
# https://networkx.github.io/documentation/stable/tutorial.html
# https://networkx.github.io/documentation/stable/reference/functions.html

import numpy as np
from scipy import integrate
from matplotlib import pyplot as plt
import networkx as nx
import time
from random import random

tstart = time.time()

plt.close('all')

betap = 0.014;
mu = 0.13;

print('beta = ',betap)
print('betap/mu = ',betap/mu)


N = 128      # 50


facoef = 2
k = 1
nodecouple = nx.barabasi_albert_graph(N, k, seed=None)

indhi = 0
deg = 0
for omloop in nodecouple.node:
    degtmp = nodecouple.degree(omloop)
    if degtmp > deg:
        deg = degtmp
        indhi = omloop
print('highest degree node = ',indhi)
print('highest degree = ',deg)

plt.figure(1)
colors = [(random(), random(), random()) for _i in range(10)]
nx.draw_circular(nodecouple,node_size=75, node_color=colors)
print(nx.info(nodecouple))
        
# function: omegout, yout = coupleN(G)
def coupleN(G,tlim):

    # function: yd = flow_deriv(x_y)
    def flow_deriv(x_y,t0):
        
        N = np.int(x_y.size/2)
        yd = np.zeros(shape=(2*N,))
        ind = -1
        for omloop in G.node:
            ind = ind + 1
            temp1 = -mu*x_y[ind] + betap*x_y[ind]*x_y[N+ind]
            temp2 =  -betap*x_y[ind]*x_y[N+ind]
            linksz = G.node[omloop]['numlink']
            for cloop in range(linksz):
                cindex = G.node[omloop]['link'][cloop]
                indx = G.node[cindex]['index']
                g = G.node[omloop]['coupling'][cloop]
                
                temp1 = temp1 + g*betap*x_y[indx]*x_y[N+ind]
                temp2 = temp2 - g*betap*x_y[indx]*x_y[N+ind]
            
            yd[ind] = temp1
            yd[N+ind] = temp2
                
        return yd
    # end of function flow_deriv(x_y)
    x0 = x_y
    t = np.linspace(0,tlim,tlim)      # 600  300
    y = integrate.odeint(flow_deriv, x0, t)        
    
    return t,y
    # end of function: omegout, yout = coupleN(G)

lnk = np.zeros(shape = (N,), dtype=int)
ind = -1
for loop in nodecouple.node:
    ind = ind + 1
    nodecouple.node[loop]['index'] = ind
    nodecouple.node[loop]['link'] = list(nx.neighbors(nodecouple,loop))
    nodecouple.node[loop]['numlink'] = len(list(nx.neighbors(nodecouple,loop)))
    lnk[ind] = len(list(nx.neighbors(nodecouple,loop)))

gfac = 0.1

ind = -1
for nodeloop in nodecouple.node:
    ind = ind + 1
    nodecouple.node[nodeloop]['coupling'] = np.zeros(shape=(lnk[ind],))
    for linkloop in range (lnk[ind]):
        nodecouple.node[nodeloop]['coupling'][linkloop] = gfac*facoef
            
x_y = np.zeros(shape=(2*N,))   
for loop in nodecouple.node:
    x_y[loop]=0
    x_y[N+loop]=nodecouple.degree(loop)
    #x_y[N+loop]=1
x_y[N-1 ]= 0.01
x_y[2*N-1] = x_y[2*N-1] - 0.01
N0 = np.sum(x_y[N:2*N]) - x_y[indhi] - x_y[N+indhi]
print('N0 = ',N0)
     
tlim0 = 600
t0,yout0 = coupleN(nodecouple,tlim0)                           # Here is the subfunction call for the flow


plt.figure(2)
plt.yscale('log')
plt.gca().set_ylim(1e-3, 1)
for loop in range(N):
    lines1 = plt.plot(t0,yout0[:,loop])
    lines2 = plt.plot(t0,yout0[:,N+loop])
    lines3 = plt.plot(t0,N0-yout0[:,loop]-yout0[:,N+loop])

    plt.setp(lines1, linewidth=0.5)
    plt.setp(lines2, linewidth=0.5)
    plt.setp(lines3, linewidth=0.5)
    

Itot = np.sum(yout0[:,0:127],axis = 1) - yout0[:,indhi]
Stot = np.sum(yout0[:,128:255],axis = 1) - yout0[:,N+indhi]
Rtot = N0 - Itot - Stot
plt.figure(3)
#plt.plot(t0,Itot,'r',t0,Stot,'g',t0,Rtot,'b')
plt.plot(t0,Itot/N0,'r',t0,Rtot/N0,'b')
#plt.legend(('Infected','Susceptible','Removed'))
plt.legend(('Infected','Removed'))
plt.hold

# Repeat but innoculate highest-degree node
x_y = np.zeros(shape=(2*N,))   
for loop in nodecouple.node:
    x_y[loop]=0
    x_y[N+loop]=nodecouple.degree(loop)
    #x_y[N+loop]=1
x_y[N-1] = 0.01
x_y[2*N-1] = x_y[2*N-1] - 0.01
N0 = np.sum(x_y[N:2*N]) - x_y[indhi] - x_y[N+indhi]
     
tlim0 = 50
t0,yout0 = coupleN(nodecouple,tlim0)


# remove all edges from highest-degree node
ee = list(nodecouple.edges(indhi))
nodecouple.remove_edges_from(ee)
print(nx.info(nodecouple))

#nodecouple.remove_node(indhi)        
lnk = np.zeros(shape = (N,), dtype=int)
ind = -1
for loop in nodecouple.node:
    ind = ind + 1
    nodecouple.node[loop]['index'] = ind
    nodecouple.node[loop]['link'] = list(nx.neighbors(nodecouple,loop))
    nodecouple.node[loop]['numlink'] = len(list(nx.neighbors(nodecouple,loop)))
    lnk[ind] = len(list(nx.neighbors(nodecouple,loop)))

ind = -1
x_y = np.zeros(shape=(2*N,)) 
for nodeloop in nodecouple.node:
    ind = ind + 1
    nodecouple.node[nodeloop]['coupling'] = np.zeros(shape=(lnk[ind],))
    x_y[ind] = yout0[tlim0-1,nodeloop]
    x_y[N+ind] = yout0[tlim0-1,N+nodeloop]
    for linkloop in range (lnk[ind]):
        nodecouple.node[nodeloop]['coupling'][linkloop] = gfac*facoef

    
tlim1 = 500
t1,yout1 = coupleN(nodecouple,tlim1)

t = np.zeros(shape=(tlim0+tlim1,))
yout = np.zeros(shape=(tlim0+tlim1,2*N))
t[0:tlim0] = t0
t[tlim0:tlim1+tlim0] = tlim0+t1
yout[0:tlim0,:] = yout0
yout[tlim0:tlim1+tlim0,:] = yout1


plt.figure(4)
plt.yscale('log')
plt.gca().set_ylim(1e-3, 1)
for loop in range(N):
    lines1 = plt.plot(t,yout[:,loop])
    lines2 = plt.plot(t,yout[:,N+loop])
    lines3 = plt.plot(t,N0-yout[:,loop]-yout[:,N+loop])

    plt.setp(lines1, linewidth=0.5)
    plt.setp(lines2, linewidth=0.5)
    plt.setp(lines3, linewidth=0.5)
    

Itot = np.sum(yout[:,0:127],axis = 1) - yout[:,indhi]
Stot = np.sum(yout[:,128:255],axis = 1) - yout[:,N+indhi]
Rtot = N0 - Itot - Stot
plt.figure(3)
#plt.plot(t,Itot,'r',t,Stot,'g',t,Rtot,'b',linestyle='dashed')
plt.plot(t,Itot/N0,'r',t,Rtot/N0,'b',linestyle='dashed')
#plt.legend(('Infected','Susceptible','Removed'))
plt.legend(('Infected','Removed'))
plt.xlabel('Days')
plt.ylabel('Fraction of Sub-Population')
plt.title('Network Dynamics for COVID-19')
plt.show()
plt.hold()

elapsed_time = time.time() - tstart
print('elapsed time = ',format(elapsed_time,'.2f'),'secs')