Figure 4.5 (a, b, c, and d) --------------------------- :download:Downloadable Source Code  .. image:: fig4p5a.png :width: 45 % .. image:: fig4p5b.png :width: 45 % .. image:: fig4p5c.png :width: 45 % .. image:: fig4p5d.png :width: 45 % :: import EoN import networkx as nx import matplotlib.pyplot as plt import scipy from scipy import integrate def complete_graph_dX(X, t, tau, gamma, N): r'''This system is given in Proposition 2.3, taking Q=S, T=I f_{SI}(k) = f_{QT}= k*\tau f_{IS}(k) = f_{TQ} = \gamma \dot{Y}^0 = \gamma Y^1 - 0\\ \dot{Y}^1 = 2\gamma Y^2 + 0Y^0 - (\gamma + (N-1)\tau)Y^1 \dot{Y}^2 = 3\gamma Y^3 + (N-1)\tau Y^1 - (2\gamma+2(N-2))Y^2 ... \dot{Y}^N = (N-1)\tau Y^{N-1} - N\gamma Y^N Note that X has length N+1 ''' #X[k] is probability of k infections. dX = [] dX.append(gamma*X[1]) for k in range(1,N): dX.append((k+1)*gamma*X[k+1]+ (N-k+1)*(k-1)*tau*X[k-1] - ((N-k)*k*tau + k*gamma)*X[k]) dX.append((N-1)*tau*X[N-1] - N*gamma*X[N]) return scipy.array(dX) def complete_graph_lumped(N, I0, tmin, tmax, tcount): times = scipy.linspace(tmin, tmax, tcount) X0 = scipy.zeros(N+1) #length N+1 of just 0 entries X0[I0]=1. #start with 100 infected. X = integrate.odeint(complete_graph_dX, X0, times, args = (tau, gamma, N)) #X[t] is array whose kth entry is p(k infected| time=t). I = scipy.array([sum(k*Pkt[k] for k in range(len(Pkt))) for Pkt in X]) S = N-I return times, S, I N=200 gamma = 1 k = N-1. tau_c = gamma/k rho = 0.1 for tau, label in zip([0.9*tau_c, tau_c, 1.2*tau_c, 1.5*tau_c],['a', 'b', 'c', 'd']): plt.clf() t, S, I = complete_graph_lumped(N, int(N*rho), 0 , 20, 1001) plt.plot(t, I) S0 = (1-rho)*N I0 = rho*N t, S, I = EoN.SIS_homogeneous_meanfield(S0, I0, k, tau, gamma, tmin=0, tmax=20, tcount=1001) plt.plot(t, I, '--') S0 = (1-rho)*N I0 = rho*N SI0 = (1-rho)*N*k*rho SS0 = (1-rho)*N*k*(1-rho) t, S, I = EoN.SIS_homogeneous_pairwise(S0, I0, SI0, SS0, k, tau, gamma, tmin = 0, tmax=20, tcount=1001) plt.plot(t, I, ':') plt.xlabel('$t$') plt.ylabel('Prevalence') plt.savefig('fig4p5{}.png'.format(label))