Main

ModeloSIR.py

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+# Author: Lucas Costa Fernandes
+# Linkedin: https://www.linkedin.com/in/lucascostafernandes/
+# GitHub: https://github.com/LucaCosta
+# Email: [email protected]
+
+# O modelo SIR para disseminação de doenças. Baseado no artigo
+# "The SIR Model for Spread of Disease - The Differential Equation Model"
+# Author(s): David Smith and Lang Moore"
+
+# Importando bibliotecas
+import numpy as np
+from scipy.integrate import odeint
+import matplotlib.pyplot as plt
+
+# Total population, N.
+N = 7900000
+# Initial number of infected and recovered individuals, I0 and R0.
+I0, R0 = 10, 0
+# Everyone else, S0, is susceptible to infection initially.
+S0 = N - I0 - R0
+# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).
+beta, gamma = 1/2, 1/3 
+# A grid of time points (in days)
+t = np.linspace(0, 160,160)
+# The SIR model differential equations.
+def deriv(y, t, N, beta, gamma):
+    S, I, R = y
+    dSdt = (-beta * S * I) / N
+    dIdt = (beta * S * I) / N - gamma * I
+    dRdt = gamma * I
+    return dSdt, dIdt, dRdt
+# Initial conditions vector
+y0 = S0, I0, R0
+# Integrate the SIR equations over the time grid, t.
+ret = odeint(deriv, y0, t, args=(N, beta, gamma))
+S, I, R = ret.T
+# Plot the data on three separate curves for S(t), I(t) and R(t)
+fig = plt.figure(facecolor='w')
+ax = fig.add_subplot(111, facecolor='#dddddd', axisbelow=True)
+plt.title ('Modelo SIR')
+plt.figure(figsize=(8, 8))
+ax.plot(t, S/N, 'b', alpha=0.5, lw=2, label='Susceptible')
+ax.plot(t, I/N, 'r', alpha=0.5, lw=2, label='Infected')
+ax.plot(t, R/N, 'g', alpha=0.5, lw=2, label='Recovered with immunity')
+ax.set_xlabel('Time /days')
+ax.set_ylabel('Number (1000s)')
+ax.set_ylim(0,1.2)
+ax.yaxis.set_tick_params(length=0)
+ax.xaxis.set_tick_params(length=0)
+ax.grid(b=True, which='major', c='w', lw=2, ls='-')
+legend = ax.legend()
+legend.get_frame().set_alpha(0.5)
+for spine in ('top', 'right', 'bottom', 'left'):
+    ax.spines[spine].set_visible(False)
+plt.show()

RungeKutta5.py

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+import numpy as np
+import pylab as plt
+
+def f(P,t):
+    r=0.8
+    K=100
+    valor = r*P*(1-P/K)
+    return valor
+
+a=0
+b= 100
+Num = 100 # Para diminuir o erro deve-se aumentar o valor de Num
+h =(b-a)/Num
+P = 0.5 # Xn
+
+t_pontos  = np.arange(a,b,h)
+P_pontos =[]
+# Method of Runge kutta 5th
+
+for i in t_pontos:
+    P_pontos.append(P)
+    k1 = h*f(P,i)
+    k2 = h*f(P + h/4, i + k1/4)
+    k3 = h*f(P + (3/8 * h), i + (3/32 * k1) + (9/32 * k2))
+    k4 = h*f(P + (12/13 * h), i + (1932/2197 * k1) - (7200/2197 * k2) + (7296/2197 * k3))
+    k5 = h*f(P + h, i + (439/216 * k1) - (8 * k2) + (3680/513) * k3 - (845/4104 * k4))
+    P = P + (25/216 * k1) + (1408/2565 * k3) + (2197/4104 * k4) - k5/5
+
+
+print(P_pontos[1])
+
+plt.plot(t_pontos,P_pontos,color='#FF4500',linewidth=1.5, label='função dP/dt=P')
+plt.ylim(0,110)
+plt.title('Gráfico da função sigmóide')
+plt.xlabel('t')
+plt.ylabel('P(t)')
+plt.grid(True)
+plt.show()

RungeKutta_4ordem.py

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+# This code is a solution for the differential equation dP/dt =P 
+
+# Method of Runge Kutta 4th
+
+import numpy as np
+import pylab as plt
+
+def f(P,t):
+    valor = 10*np.exp(-((t-2)**2)/(2*(0.075)**2)) - 0.6 * P
+    return valor
+
+a=0
+b= 4
+Num = 100 # Para diminuir o erro deve-se aumentar o valor de Num
+h =(b-a)/Num
+P = 0.5
+
+t_pontos  = np.arange(a,b,h)
+P_pontos =[]
+# Method of Runge kutta 4th
+
+for i in t_pontos:
+    P_pontos.append(P)
+    k1 = h * f(P,i)
+    k2 = h * f(P+0.5*k1, i+0.5*h)
+    k3 = h * f(P+0.5*k2,i+0.5*h)
+    k4 = h * f(P+k3,i+h)
+    P += (k1+2*k2+2*k3+k4)/6
+
+print(P_pontos[1])
+
+plt.plot(t_pontos,P_pontos,color='#FF4500',linewidth=1.5, label='função dP/dt=P')
+plt.title('Gráfico da função resolução do problema')
+plt.xlabel('t')
+plt.ylabel('P(t)')
+plt.grid(True)
+plt.show()