Merge branch 'covid' of ssh://ssh.hesge.ch:10572/orestis.malaspin/math_tech_info into covid

covid/python/covid.py

@@ -6,6 +6,22 @@ swiss = np.array([18, 27, 42, 56, 90, 114, 214, 268, 337, 374, 491, 652, 858, 11
 
 days = np.array(range(1,len(swiss)+1))
 
+def F(yx, yy, yz, t):
+    return sigma * (yy - yz), rho * yx, (mu * yx + yz)
+
+def rk2(yx, yy, yz, t, dt):
+    yx_tmp, yy_tmp, yz_tmp = F(yx, yy, yz, t)
+    yx0 = yx + dt / 2 * yx_tmp
+    yy0 = yy + dt / 2 * yy_tmp
+    yz0 = yz + dt / 2 * yz_tmp
+
+    y1x, y1y, y1z = F(yx0, yy0, yz0, t+dt/2)
+
+    return yx + dt * y1x, yy + dt * y1y, yz + dt * y1z
+
+def yx(dt, yx0, yy0, yz0, sig):
+    return yx0 + dt * sigma * (yy0-yz0)
+
 def s(dt, beta, S0, I0, N):
     return S0 - dt * (beta * S0 * I0 / N)
 

covid/python/seir.py

 import numpy as np
 import matplotlib.pyplot as plt
 import functools
+import matplotlib.animation as animation
 
 swiss = np.array([2.100350058, 3.150525088, 4.900816803, 6.534422404, 10.501750292, 13.302217036, 24.970828471, 31.271878646, 39.323220537, 43.640606768, 57.292882147, 76.079346558, 100.116686114, 131.271878646, 158.576429405, 256.709451575, 256.709451575, 268.378063011, 309.218203034, 353.325554259, 453.675612602])
 swiss = np.array([18, 27, 42, 56, 90, 114, 214, 268, 337, 374, 491, 652, 858, 1125, 1359, 2200, 2200, 2300, 2650, 3028, 3888])
 
 days = np.array(range(1,len(swiss)+1))
 
+def update(i, lines, t, p):
+    n_pop, length = p.shape
+    for j in range(0, n_pop):
+        lines[j].set_data(t[0:i], p[j][0:i])
+    return lines
+
+# def policy_r0(R_0, R_target, t, delta_t):
+#     if (t <= )
+
+
+
 def seir(y, t, R_0, Tinf, Tinc):
     N = np.sum(y)
     y1 = np.zeros(4)
@@ -16,6 +28,18 @@ def seir(y, t, R_0, Tinf, Tinc):
     y1[3] = 1.0 / Tinf * y[2]
 
     return y1
+
+def seihse(y, t, R_0, Tinf, Tinc, Thos, Tsev):
+    N = np.sum(y)
+    y1 = np.zeros(6)
+    y1[0] = - R_0 / Tinf * y[2] * y[0] / N # Sane
+    y1[1] =  R_0 / Tinf * y[2] * y[0] / N - 1.0 / Tinc * y[1] # Exposed
+    y1[2] = 1.0 / Tinc * y[1] - 1.0 / Tinf * y[2] - 1.0 / Tinf * y[2] # Infectious
+    y1[3] = 1.0 / Tinf * y[2] + 1.0 / Thos * y[4] + 1.0 / Tsev * y[5] # Recovered
+    y1[4] = - 1.0 / Thos * y[4] + 1.0 / Tinf * y[2] - 1.0 / Tsev * y[4] # Hospitalized
+    y1[5] = - 1.0 / Tsev * y[5] + 1.0 / Thos * y[4] # Severe
+
+    return y1
     
 def rk4(F, y, t, dt):
     k1 = dt * F(y, t)
@@ -30,33 +54,35 @@ R_02 = 1 - 1/R_01
 
 Tinf = 7.0
 Tinc = 5.1
+Thos = 14.0
+Tsev = 14.0
+
 N = 500000
 
 I0 = 214 / 0.2
 E0 = 2000
 R0 = 0
 S0 = N-E0-I0
+H0 = 0
+Sev0 = 0
 t0 = 24
 
 # max_t = 5*days[len(swiss)-1]
 max_t = 200.0
-n_steps = 10000
+n_steps = 1000
 dt = max_t / n_steps
 
-y0 = np.array([S0, E0, I0, R0])
+y0 = np.array([S0, E0, I0, R0, H0, Sev0])
 
 y_list = [y0]
 t_list = [t0]
 for i in range(0, n_steps):
     t = t_list[i] + dt
-    foo = functools.partial(seir, R_0=R_0, Tinf=Tinf, Tinc=Tinc)
+    # foo = functools.partial(seir, R_0=R_0, Tinf=Tinf, Tinc=Tinc)
+    foo = functools.partial(seihse, R_0=R_0, Tinf=Tinf, Tinc=Tinc, Thos=Thos, Tsev=Tsev)
     y1 = rk4(foo, y_list[i], t, dt)
     y_list.append(y1)
     t_list.append(t)
-    if (t > t0 and t <= t0 + 30) or (t >= t0 + 60 and t <= t0 + 90) :
-        R_0 = R_02
-    else:
-        R_0 = R_01
 
     if (y1[1] + y1[2] < 1):
         break
@@ -66,11 +92,30 @@ y = np.array(y_list)
 
 p = np.transpose(y)
 
-plt.semilogy(t, p[0], 'b')
-plt.semilogy(t, p[1], 'r')
-plt.semilogy(t, p[2], 'k')
-plt.semilogy(t, p[3], 'g')
-# plt.semilogy(days, swiss, 'k*')
-plt.legend(['S', 'E', 'I', 'R', 'swiss'])
+
+fig = plt.figure()
+# ax = plt.axes(xlim=(-0.1*np.max(t),np.max(t)*1.1), ylim=(-0.1*np.max(p),np.max(p)*1.1))
+ax = plt.axes(xlim=(1,np.max(t)*1.1), ylim=(1,np.max(p)*1.1))
+
+lines = [plt.semilogy([], [], 'r-')[0],
+         plt.semilogy([], [], 'b-')[0],
+         plt.semilogy([], [], 'g-')[0],
+         plt.semilogy([], [], 'k-')[0],
+         plt.semilogy([], [], 'c-')[0],
+         plt.semilogy([], [], 'y-')[0] ]
+
+# anim = animation.FuncAnimation(fig, functools.partial(update, lines=lines, t=t, p=p), 
+#            frames=n_steps, interval=10, blit=True)
+ax.legend(['Sain', 'Exposé', 'Infectieux', 'Rétablis', 'Hospitalisés', 'Soins intensifs'])
+
+anim = animation.FuncAnimation(fig, functools.partial(update, lines=lines, t=t, p=p), 
+           frames=n_steps, interval=10, blit=True)
+
+# plt.semilogy(t, p[0], 'b')
+# plt.semilogy(t, p[1], 'r')
+# plt.semilogy(t, p[2], 'k')
+# plt.semilogy(t, p[3], 'g')
+# # plt.semilogy(days, swiss, 'k*')
+# plt.legend(['S', 'E', 'I', 'R', 'swiss'])
 plt.show()
 

tpEdo/tpEquadiffs.md

@@ -166,7 +166,7 @@ et par quatre équation différentielles ordinaires
 S'(t)&=-\frac{\mathcal{R}_0}{T_{inf}}I(t)\frac{S(t)}{N},\\
 E'(t)&=\frac{\mathcal{R}_0}{T_{inf}}I(t)\frac{S(t)}{N}-\frac{1}{T_{inc}}E(t),\\
 I'(t)&=\frac{1}{T_{inc}}E(t)-\frac{1}{T_{inf}}I(t),\\
-R'(t)&=-\frac{1}{T_{inf}}I(t),
+R'(t)&=\frac{1}{T_{inf}}I(t),
 \end{align}
 où $\mathcal{R}_0$ est taux de reproduction de base, $T_{inf}$ est le temps où un individu est infectieux, et $T_{inc}$ est le temps d'incubation de la maladie. La taux de reproduction de base peut être remplacé par
 le taux de reproduction  effectif, $\mathcal{R}_t=\mathcal{R}_0\frac{S(t)}{N}$ qui représente