SEIR.py

import numpy as np
from ODESolver import RungeKutta4
import matplotlib.pyplot as plt
class Region:
    def __init__(self, name, S_0 ,E2_0):
        self.E1_0 = 0
        self.name = name
        self.S_0 = S_0
        self.E2_0 = E2_0
        self.I_0 = 0
        self.Ia_0 = 0
        self.R_0 = 0
        self.t = 0
        self.population = self.S_0 + self.E2_0

    def set_SEIR_values(self, u, t):

        self.S_0 = u[:,0]
        self.E1_0 = u[:,1]
        self.E2_0 = u[:,2]
        self.I_0 = u[:,3]
        self.Ia_0 = u[:,4]
        self.R_0 = u[:,5]
        self.t = t

    def plot(self):
        plt.plot(self.t, self.S_0, label='S(t)')
        plt.plot(self.t, self.I_0, label='I(t)')
        plt.plot(self.t, self.Ia_0, label='Ia(t)')
        plt.plot(self.t, self.R_0, label='R(t)')
        plt.xlabel('Time(days)')
        plt.ylabel('Population')
        plt.grid()



class ProblemSEIR:
    def __init__(self, region, beta, r_ia=0.1, r_e2=1.25, lmbda_1=0.33,
                 lmbda_2=0.5, p_a=0.4, mu=0.2):
        if isinstance(beta, (float, int)):
            self.beta = lambda t: beta
        elif callable(beta):
            self.beta = beta
        self.r_ia = r_ia
        self.r_e2 = r_e2
        self.lmbda_1 = lmbda_1
        self.lmbda_2 = lmbda_2
        self.p_a = p_a
        self.mu = mu
        self.region = region
        self.set_initial_condition()



    def set_initial_condition(self):
        region = self.region
        self.initial_condition = [region.S_0, region.E1_0, region.E2_0, region.I_0, region.Ia_0, region.R_0]

    def get_population(self):
        return self.region.population

    def solution(self,u,t):
        return self.region.set_SEIR_values(u, t)

    def __call__(self,u,t):

        S, E1, E2, I, Ia, R = u
        print(u)
        N = sum(u)
        dS = -self.beta(t) * S * I / N - self.r_ia * self.beta(t) * S * Ia / N - self.r_e2 * self.beta(t) * S * E2 / N
        dE1 = self.beta(t) * S * I / N + self.r_ia * self.beta(t) * S * Ia / N + self.r_e2 * self.beta(t) * S * E2 / N - self.lmbda_1 * E1
        dE2 = self.lmbda_1 * (1 - self.p_a) * E1 - self.lmbda_2 * E2
        dI = self.lmbda_2 * E2 - self.mu * I
        dIa = self.lmbda_1 * self.p_a * E1 - self.mu * Ia
        dR = self.mu * (I + Ia)

        return [dS, dE1, dE2, dI, dIa, dR]


class SolverSEIR:
    def __init__(self, problem, T, dt):
        self.problem = problem  # instance of class ProblemSEIR
        self.T = T  # final time
        self.dt = dt
        self.total_population = self.problem.get_population

    def solve(self, method=RungeKutta4):
        solver = method(self.problem)
        solver.set_initial_condition([5e6 , 0 , 100 , 0 , 0 , 0])
        # calculate the number of time steps from T and dt
        N = int(self.T/self.dt)
        t = np.linspace(0, self.T, N)
        u, t = solver.solve(t)
        self.problem.region.set_SEIR_values(u, t)
        self.problem.solution(u, t)

if __name__ == '__main__':
    nor = Region('Norway',S_0=5e6,E2_0=100)
    print(nor.name, nor.population)
    S_0, E1_0, E2_0 = nor.S_0, nor.E1_0, nor.E2_0
    I_0, Ia_0, R_0 = nor.I_0, nor.Ia_0, nor.R_0
    print(f'S_0= {S_0}, E1_0 = {E1_0}, E2_0 = {E2_0}')
    print(f'I_0 = {I_0}, Ia_0 = {Ia_0}, R_0 = {R_0}')
    u = np.zeros((2,6))
    u[0,:] = [S_0, E1_0, E2_0, I_0, Ia_0, R_0]
    nor.set_SEIR_values(u,0)
    print(nor.S_0, nor.E1_0, nor.E2_0, nor.I_0, nor.Ia_0, nor.R_0)
    problem = ProblemSEIR(nor, beta=0.5)
    problem.set_initial_condition()
    print(problem.initial_condition)
    print(problem.get_population())
    print(problem([1, 1, 1, 1, 1, 1], 0))
    solver = SolverSEIR(problem, T=100, dt=1.0)
    solver.solve()
    nor.plot()
    plt.legend()
    plt.show()
# #

"""

Run example:

user$ python3 SEIR.py

output:

Norway 5000100.0
S_0= 5000000.0, E1_0 = 0, E2_0 = 100
I_0 = 0, Ia_0 = 0, R_0 = 0
[5000000.       0.] [0. 0.] [100.   0.] [0. 0.] [0. 0.] [0. 0.]
[array([5000000.,       0.]), array([0., 0.]), array([100.,   0.]), array([0., 0.]), array([0., 0.]), array([0., 0.])]
5000100.0
[1, 1, 1, 1, 1, 1]
[-0.19583333333333333, -0.13416666666666668, -0.302, 0.3, -0.068, 0.4]
[5.e+06 0.e+00 1.e+02 0.e+00 0.e+00 0.e+00]
[5.e+06 0.e+00 1.e+02 0.e+00 0.e+00 0.e+00]
[4.99996843e+06 3.15650253e+01 7.47474747e+01 2.52525253e+01
 0.00000000e+00 0.00000000e+00]
[4.99997003e+06 2.47098053e+01 8.42808776e+01 1.63248648e+01
 2.10433502e+00 2.55076013e+00]
[4.99993844e+06 5.33205836e+01 6.23758613e+01 3.92681473e+01
 2.86952252e+00 3.72307067e+00]
[4.99993909e+06 5.16985028e+01 6.50885565e+01 3.63184676e+01
 3.44768246e+00 4.36030707e+00]
[4.99990928e+06 7.28851496e+01 5.38219026e+01 4.90864397e+01
 6.54599856e+00 8.37708990e+00]
[4.99990954e+06 6.90999562e+01 5.87856819e+01 4.49516309e+01
 7.64548045e+00 9.97974528e+00]
[4.99987889e+06 8.88640430e+01 4.92188094e+01 5.69270684e+01
 1.11164684e+01 1.49859861e+01]
[4.99987932e+06 8.78770249e+01 5.06603104e+01 5.54256952e+01
 1.14357131e+01 1.52784480e+01]
[4.99984905e+06 1.03505946e+02 4.66550052e+01 6.26201478e+01
 1.61390589e+01 2.20321256e+01]
[4.99984838e+06 1.01572160e+02 4.92293380e+01 6.08819947e+01
 1.67059015e+01 2.32339234e+01]
[4.99981665e+06 1.16687827e+02 4.61114404e+01 6.79896044e+01
 2.16037382e+01 3.09527705e+01]
[4.99981695e+06 1.16093763e+02 4.68630969e+01 6.72415709e+01
 2.17719599e+01 3.10747092e+01]
[4.99978463e+06 1.29065608e+02 4.66383578e+01 7.22836084e+01
 2.73123562e+01 4.00659749e+01]
[4.99978329e+06 1.28245551e+02 4.79922947e+01 7.17175594e+01
 2.76175099e+01 4.11349076e+01]
[4.99974905e+06 1.41254923e+02 4.82736744e+01 7.69917078e+01
 3.32920718e+01 5.11424000e+01]
[4.99974926e+06 1.40897951e+02 4.86562317e+01 7.66274153e+01
 3.33738824e+01 5.11810856e+01]
[4.99971371e+06 1.52964256e+02 5.04590996e+01 8.11741995e+01
 3.93959799e+01 6.22923278e+01]
[4.99971185e+06 1.52822146e+02 5.12104605e+01 8.11701980e+01
 3.95921076e+01 6.33598916e+01]
[4.99967394e+06 1.65275875e+02 5.33567920e+01 8.60932644e+01
 4.57517630e+01 7.55775109e+01]
[4.99967412e+06 1.65058533e+02 5.35447436e+01 8.59193642e+01
 4.57850257e+01 7.55754053e+01]
[4.99963437e+06 1.77300138e+02 5.65291971e+01 9.07620405e+01
 5.21641779e+01 8.88788790e+01]
[4.99963204e+06 1.77585388e+02 5.69997077e+01 9.10265311e+01
 5.23359261e+01 9.00123970e+01]
[4.99958952e+06 1.90456374e+02 6.02740901e+01 9.63178972e+01
 5.88901631e+01 1.04537518e+02]
[4.99958967e+06 1.90319063e+02 6.03609555e+01 9.62350950e+01
 5.88965859e+01 1.04514456e+02]
[4.99954484e+06 2.03437053e+02 6.41501963e+01 1.01757044e+02
 6.56353733e+01 1.20184323e+02]
[4.99954208e+06 2.04010714e+02 6.45051163e+01 1.02156150e+02
 6.58292204e+01 1.21422781e+02]
[4.99949404e+06 2.17946470e+02 6.85847568e+01 1.08175830e+02
 7.27991821e+01 1.38450894e+02]
[4.99949419e+06 2.17853347e+02 6.86198314e+01 1.08134204e+02
 7.27909074e+01 1.38415542e+02]
[4.99944339e+06 2.32343372e+02 7.30769259e+01 1.14539797e+02
 7.99618470e+01 1.56690806e+02]
[4.99944018e+06 2.33133000e+02 7.34003994e+01 1.15018296e+02
 8.02035113e+01 1.58062173e+02]
[4.99938572e+06 2.48607399e+02 7.81755226e+01 1.21969093e+02
 8.76725779e+01 1.77854291e+02]
[4.99938587e+06 2.48537155e+02 7.81842874e+01 1.21944154e+02
 8.76561836e+01 1.77809943e+02]
[4.99932819e+06 2.64792958e+02 8.32944960e+01 1.29370070e+02
 9.53711673e+01 1.98981694e+02]
[4.99932451e+06 2.65765549e+02 8.36296197e+01 1.29910434e+02
 9.56755962e+01 2.00511078e+02]
[4.99926265e+06 2.83169433e+02 8.91002155e+01 1.37936804e+02
 1.03763187e+02 2.23382878e+02]
[4.99926281e+06 2.83109441e+02 8.90955174e+01 1.37916877e+02
 1.03742065e+02 2.23330308e+02]
[4.99919725e+06 3.01484384e+02 9.49075935e+01 1.46484747e+02
 1.12137031e+02 2.47740302e+02]
[4.99919304e+06 3.02630491e+02 9.52773918e+01 1.47087002e+02
 1.12514051e+02 2.49453720e+02]
[4.99912271e+06 3.22325956e+02 1.01501721e+02 1.56322226e+02
 1.21362686e+02 2.75774965e+02]
[4.99912289e+06 3.22268673e+02 1.01489809e+02 1.56301908e+02
 1.21338431e+02 2.75713794e+02]
[4.99904833e+06 3.43112861e+02 1.08087937e+02 1.66142576e+02
 1.30566602e+02 3.03758272e+02]
[4.99904353e+06 3.44437502e+02 1.08506162e+02 1.66814763e+02
 1.31024076e+02 3.05684418e+02]
[4.99896355e+06 3.66791123e+02 1.15576218e+02 1.77403048e+02
 1.40793921e+02 3.35883256e+02]
[4.99896375e+06 3.66731907e+02 1.15559956e+02 1.77379885e+02
 1.40767126e+02 3.35812560e+02]
[4.99887894e+06 3.90415531e+02 1.23051340e+02 1.88644532e+02
 1.50997018e+02 3.67948621e+02]
[4.99887348e+06 3.91933129e+02 1.23527938e+02 1.89398453e+02
 1.51542604e+02 3.70119787e+02]
[4.99878250e+06 4.17337320e+02 1.31558734e+02 2.01505419e+02
 1.62410209e+02 4.04689541e+02]
[4.99878272e+06 4.17273135e+02 1.31539275e+02 2.01478264e+02
 1.62380909e+02 4.04608110e+02]
[4.99868625e+06 4.44202303e+02 1.40049600e+02 2.14343913e+02
 1.73797006e+02 4.41361562e+02]
[4.99868003e+06 4.45934013e+02 1.40593444e+02 2.15193424e+02
 1.74439142e+02 4.43814264e+02]
[4.99857653e+06 4.74821983e+02 1.49719287e+02 2.29011635e+02
 1.86598546e+02 4.83321760e+02]
[4.99857678e+06 4.74750635e+02 1.49696933e+02 2.28979848e+02
 1.86566463e+02 4.83228188e+02]
[4.99846702e+06 5.05379372e+02 1.59369741e+02 2.43652826e+02
 1.99371408e+02 5.25202563e+02]
[4.99845995e+06 5.07351800e+02 1.59989986e+02 2.44613336e+02
 2.00119895e+02 5.27978111e+02]
[4.99834220e+06 5.40209335e+02 1.70364270e+02 2.60366036e+02
 2.13785108e+02 5.73073286e+02]
[4.99834249e+06 5.40129026e+02 1.70338901e+02 2.60329122e+02
 2.13749781e+02 5.72965979e+02]
[4.99821763e+06 5.74969609e+02 1.81336929e+02 2.77048125e+02
 2.28167496e+02 6.20852737e+02]
[4.99820957e+06 5.77214347e+02 1.82043708e+02 2.78136617e+02
 2.29033867e+02 6.23997860e+02]
[4.99807562e+06 6.14590298e+02 1.93840504e+02 2.96081173e+02
 2.44442226e+02 6.75424663e+02]
[4.99807595e+06 6.14499366e+02 1.93811785e+02 2.96038614e+02
 2.44403076e+02 6.75301821e+02]
[4.99793390e+06 6.54132263e+02 2.06319352e+02 3.15078094e+02
 2.60682521e+02 7.29891891e+02]
[4.99792474e+06 6.56685914e+02 2.07124165e+02 3.16313390e+02
 2.61680325e+02 7.33459459e+02]
[4.99777235e+06 6.99202547e+02 2.20540804e+02 3.36745083e+02
 2.79096485e+02 7.92068229e+02]
[4.99777272e+06 6.99099307e+02 2.20508278e+02 3.36696270e+02
 2.79052840e+02 7.91927812e+02]
[4.99761111e+06 7.44183489e+02 2.34734300e+02 3.58370455e+02
 2.97472305e+02 8.54124692e+02]
[4.99760070e+06 7.47087996e+02 2.35650288e+02 3.59773573e+02
 2.98617365e+02 8.58174555e+02]
[4.99742733e+06 7.95451880e+02 2.50910580e+02 3.83030038e+02
 3.18337832e+02 9.24936082e+02]
[4.99742775e+06 7.95334524e+02 2.50873703e+02 3.82974241e+02
 3.18288939e+02 9.24775771e+02]
[4.99724391e+06 8.46618664e+02 2.67055210e+02 4.07641919e+02
 3.39160842e+02 9.95610435e+02]
[4.99723206e+06 8.49921846e+02 2.68097385e+02 4.09236474e+02
 3.40471512e+02 1.00021039e+03]
[4.99703484e+06 9.04935768e+02 2.85455353e+02 4.35702925e+02
 3.62829728e+02 1.07623193e+03]
[4.99703532e+06 9.04802295e+02 2.85413507e+02 4.35639280e+02
 3.62774746e+02 1.07604908e+03]
[4.99682619e+06 9.63137195e+02 3.03819619e+02 4.63709430e+02
 3.86450986e+02 1.15669696e+03]
[4.99681271e+06 9.66893439e+02 3.05005101e+02 4.65522070e+02
 3.87948440e+02 1.16192387e+03]
[4.99658836e+06 1.02946967e+03 3.24749215e+02 4.95637398e+02
 4.13320449e+02 1.24846737e+03]
[4.99658890e+06 1.02931784e+03 3.24701706e+02 4.95564894e+02
 4.13258446e+02 1.24825897e+03]
[4.99635099e+06 1.09567038e+03 3.45638109e+02 5.27503214e+02
 4.40136358e+02 1.34005931e+03]
[4.99633566e+06 1.09994147e+03 3.46986393e+02 5.29564092e+02
 4.41844921e+02 1.34600034e+03]
[4.99608045e+06 1.17111669e+03 3.69444346e+02 5.63827902e+02
 4.70655708e+02 1.44450322e+03]
[4.99608107e+06 1.17094395e+03 3.69390393e+02 5.63745373e+02
 4.70585642e+02 1.44426584e+03]
[4.99581044e+06 1.24641285e+03 3.93204385e+02 6.00081798e+02
 5.01114669e+02 1.54874372e+03]
[4.99579301e+06 1.25126890e+03 3.94737641e+02 6.02425087e+02
 5.03062189e+02 1.55549781e+03]
[4.99550270e+06 1.33222102e+03 4.20281728e+02 6.41405780e+02
 5.35792771e+02 1.66759661e+03]
[4.99550340e+06 1.33202450e+03 4.20220452e+02 6.41311888e+02
 5.35713476e+02 1.66732635e+03]
[4.99519557e+06 1.41785807e+03 4.47306627e+02 6.82649186e+02
 5.70402637e+02 1.78621780e+03]
[4.99517574e+06 1.42337865e+03 4.49050040e+02 6.85313644e+02
 5.72620920e+02 1.79389724e+03]
[4.99484552e+06 1.51544585e+03 4.78103233e+02 7.29657637e+02
 6.09816303e+02 1.92145455e+03]
[4.99484632e+06 1.51522227e+03 4.78033645e+02 7.29550857e+02
 6.09726473e+02 1.92114696e+03]
[4.99449617e+06 1.61283853e+03 5.08840305e+02 7.76574418e+02
 6.49152759e+02 2.05642750e+03]
[4.99447362e+06 1.61911386e+03 5.10822472e+02 7.79604023e+02
 6.51678057e+02 2.06515981e+03]
[4.99409802e+06 1.72381605e+03 5.43865270e+02 8.30046242e+02
 6.93956189e+02 2.21029485e+03]
[4.99409893e+06 1.72356169e+03 5.43786255e+02 8.29924836e+02
 6.93854358e+02 2.20994488e+03]
[4.99370066e+06 1.83457109e+03 5.78822662e+02 8.83413806e+02
 7.38672172e+02 2.36386197e+03]
[4.99367502e+06 1.84170342e+03 5.81076025e+02 8.86858458e+02
 7.41545746e+02 2.37379195e+03]
[4.99324782e+06 1.96076654e+03 6.18654200e+02 9.44234251e+02
 7.89607593e+02 2.53891543e+03]
[4.99324885e+06 1.96047716e+03 6.18564501e+02 9.44096249e+02
 7.89492109e+02 2.53851732e+03]
[4.99279588e+06 2.08670821e+03 6.58409061e+02 1.00493615e+03
 8.40443909e+02 2.71362725e+03]
[4.99276673e+06 2.09481338e+03 6.60970407e+02 1.00885246e+03
 8.43712665e+02 2.72491934e+03]
[4.99228086e+06 2.23019677e+03 7.03703739e+02 1.07411111e+03
 8.98353557e+02 2.91277290e+03]
[4.99228203e+06 2.22986756e+03 7.03601942e+02 1.07395427e+03
 8.98222563e+02 2.91232013e+03]
[4.99176686e+06 2.37339574e+03 7.48911440e+02 1.14315130e+03
 9.56150848e+02 3.11152991e+03]
[4.99173373e+06 2.38260489e+03 7.51822465e+02 1.14760350e+03
 9.59868051e+02 3.12437085e+03]
[4.99118117e+06 2.53653216e+03 8.00414604e+02 1.22182350e+03
 1.02199048e+03 3.33807195e+03]
[4.99118250e+06 2.53615765e+03 8.00299116e+02 1.22164530e+03
 1.02184188e+03 3.33755710e+03]
[4.99059663e+06 2.69933800e+03 8.51819145e+02 1.30034252e+03
 1.08770271e+03 3.56417197e+03]
[4.99055897e+06 2.70979949e+03 8.55127072e+02 1.30540342e+03
 1.09192879e+03 3.57877379e+03]
[4.98993060e+06 2.88479327e+03 9.10376654e+02 1.38980980e+03
 1.16255681e+03 3.82186664e+03]
[4.98993211e+06 2.88436723e+03 9.10245686e+02 1.38960737e+03
 1.16238826e+03 3.82128130e+03]
[4.98926588e+06 3.06987101e+03 9.68822388e+02 1.47910301e+03
 1.23726645e+03 4.07905864e+03]
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Plots attached


"""