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| # %matplotlib qt | |
| import numpy as np | |
| import seaborn as sns | |
| from matplotlib import pyplot as plt | |
| from matplotlib import style | |
| style.use('default') | |
| TOTAL_POP = 100_000 | |
| MAX_ITERS = 100_000 | |
| rho = 0.5 | |
| gamma = 0.25 | |
| delta = 0.25 | |
| beta = 0.25 # Not in their paper, but this seems to fit | |
| def simul(N, xs, sigma): | |
| # We start with 50 infected individuals, 25 in each class | |
| S = N - 50 | |
| E = np.array([25., 25.]) | |
| I = np.array([25., 25.]) | |
| R = np.array([0., 0.]) | |
| Evol = [] | |
| for _ in range(MAX_ITERS): | |
| EIeff = np.sum(xs * (rho * E + I) * N/TOTAL_POP) | |
| for xi,xf in enumerate(xs): | |
| lam = beta / N[xi] * EIeff | |
| dS = - lam * xf * S[xi] | |
| dE = lam * xf * S[xi] - delta * E[xi] | |
| dI = delta * E[xi] - gamma * I[xi] | |
| dR = gamma * I[xi] | |
| S[xi] += dS | |
| E[xi] += dE | |
| I[xi] += dI | |
| R[xi] += dR | |
| dS0 = sigma * (S[1] - S[0]) | |
| S += [dS0, -dS0] | |
| Evol.append((S.copy(), E.copy(), I.copy(), R.copy())) | |
| # Do at least 1 year, then stop once nobody is getting infected. | |
| if len(Evol) > 365 and np.abs(Evol[-1][0] - Evol[-2][0]).sum() < 1: | |
| break | |
| return np.array(Evol) | |
| for title,args in [ | |
| ('Traditional', (np.array([TOTAL_POP/2, TOTAL_POP/2], float), np.array([1,1], float), 0)), | |
| ('Two classes (no big diff)', (np.array([TOTAL_POP/2, TOTAL_POP/2], float), np.array([0.5,1.5], float), 0)), | |
| ('Two classes (minority)', (np.array([TOTAL_POP/5* 4, TOTAL_POP/5], float), np.array([0.25,4.0], float), 0)), | |
| ('Two classes (minority; 1% shift)', (np.array([TOTAL_POP/5* 4, TOTAL_POP/5], float), np.array([0.25,4.0], float), .01)), | |
| ('Two classes (minority; 0.1% shift)', (np.array([TOTAL_POP/5* 4, TOTAL_POP/5], float), np.array([0.25,4.0], float), .001)), | |
| ]: | |
| N,xs,s = args | |
| mu_x = np.sum(N/np.sum(N)*xs) | |
| std_x = np.sum( N/np.sum(N)*(xs-mu_x)**2) | |
| Evol = simul(*args) | |
| fig,ax = plt.subplots() | |
| ax.plot(Evol[:,0,:].sum(1)/TOTAL_POP, label='S') | |
| ax.plot(Evol[:,1,:].sum(1)/TOTAL_POP, label='E') | |
| ax.plot(Evol[:,2,:].sum(1)/TOTAL_POP, label='I') | |
| ax.plot(Evol[:,3,:].sum(1)/TOTAL_POP, label='R') | |
| ax.legend(loc='best') | |
| ax.set_xlim(0, 365) | |
| ax.set_title(title + ' (CV={})'.format(std_x/mu_x)) | |
| sns.despine(fig, trim=True) | |
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