def simulate(beta, nu, p0, S0, I0, V_T):
p = lambda t: p0 if 6 <= t <= 6 + V_T else 0
solver = odespy.Euler(f, f_args=(beta, nu, p))
solver.set_initial_condition([S0, I0, 0, 0])
dt = 0.5 # t counts days
T = 60
N = int(T / dt)
t = np.linspace(0, T, N + 1)
u, t = solver.solve(t)
I = u[:, 1]
return I.max()
def get_solver(self, func):
"""
Returns the solver method from odespy package.
Args:
func: function
function with ODE system.
Returns: an instance of odeSolver
"""
if self.solverMethod is solverMethod.LSODA:
solver = odespy.Lsoda(func)
elif self.solverMethod is solverMethod.LSODAR:
solver = odespy.Lsodar(func)
elif self.solverMethod is solverMethod.LSODE:
solver = odespy.Lsode(func)
elif self.solverMethod is solverMethod.HEUN:
solver = odespy.Heun(func)
elif self.solverMethod is solverMethod.EULER:
solver = odespy.Euler(func)
elif self.solverMethod is solverMethod.RK4:
solver = odespy.RK4(func)
elif self.solverMethod is solverMethod.DORMAN_PRINCE:
solver = odespy.DormandPrince(func)
elif self.solverMethod is solverMethod.RKFehlberg:
solver = odespy.RKFehlberg(func)
elif self.solverMethod is solverMethod.Dopri5:
solver = odespy.Dopri5(func)
elif self.solverMethod is solverMethod.Dop853:
solver = odespy.Dop853(func)
elif self.solverMethod is solverMethod.Vode:
solver = odespy.Vode(func)
elif self.solverMethod is solverMethod.AdamsBashforth2:
solver = odespy.AdamsBashforth2(func, method='bdf')
elif self.solverMethod is solverMethod.Radau5:
solver = odespy.Radau5(func)
elif self.solverMethod is solverMethod.AdamsBashMoulton2:
solver = odespy.AdamsBashMoulton2(func)
# update default parameters
solver.nsteps = SolverConfigurations.N_STEPS
solver.atol = SolverConfigurations.ABSOLUTE_TOL
solver.rtol = SolverConfigurations.RELATIVE_TOL
return solver
import odespy
import numpy as np
import sys
I0 = 1
S0 = 1500.
period = 360
beta = lambda t: 0.0003 * np.sin(np.pi / period * t)**6
nu = 1. / 10
mu = 1. / 100
rho = 1. / 150
p = lambda t: 0.01 * np.sin(np.pi / period * (t - 50))**6
p = lambda t: 0.0
solver = odespy.Euler(f, f_args=(beta, nu, p, mu, rho))
solver.set_initial_condition([S0, I0, 0, 0])
dt = 0.5 # t counts days
T = 1400
N = int(T / dt)
t = np.linspace(0, T, N + 1)
u, t = solver.solve(t)
S, I, R, V = u[:, 0], u[:, 1], u[:, 2], u[:, 3]
from matplotlib.pyplot import *
plot(t, S, 'r-', t, I, 'b-', t, R, 'g-', t, V, 'y-')
legend(['S', 'I', 'R', 'V'])
savefig('tmppng')
savefig('tmp.pdf')
show()
return [-beta(t)*S*I,
beta(t)*S*I - nu*I,
nu*I]
import odespy
import numpy as np
import sys
# beta = 0.0005; nu = 0.1; I0 = 1
# beta = 0.0001; nu = 0.1; I0 = 1 and 50
beta = lambda t: 0.0005 if t < 12 else 0.00005
nu = 0.1
I0 = 1
S0 = 1500.
solver = odespy.Euler(f, f_args=(beta, nu))
solver.set_initial_condition([S0, I0, 0])
dt = 0.5 # t counts days
T = 60
N = int(T/dt)
t = np.linspace(0, T, N+1)
u, t = solver.solve(t)
S, I, R = u[:,0], u[:,1], u[:,2]
from matplotlib.pyplot import *
plot(t, S, 'r-',
t, I, 'b-',
t, R, 'g-')
legend(['S', 'I', 'R'])
savefig('tmppng'); savefig('tmp.pdf')
show()
rtol = 1E-5
adams_or_bdf = 'bdf'
import odespy
solvers = [
odespy.AdamsBashMoulton2(problem),
odespy.AdamsBashMoulton3(problem),
odespy.AdamsBashforth2(problem),
odespy.AdamsBashforth3(problem),
odespy.AdamsBashforth4(problem),
odespy.AdaptiveResidual(problem, solver='Euler'),
odespy.Backward2Step(problem),
odespy.BackwardEuler(problem),
odespy.Dop853(problem, rtol=rtol, atol=atol),
odespy.Dopri5(problem, rtol=rtol, atol=atol),
odespy.Euler(problem),
odespy.Heun(problem),
odespy.Leapfrog(problem),
odespy.LeapfrogFiltered(problem),
odespy.MidpointImplicit(problem),
odespy.MidpointIter(problem, max_iter=10, eps_iter=1E-7),
odespy.RK2(problem),
odespy.RK3(problem),
odespy.RK4(problem),
odespy.RKFehlberg(problem, rtol=rtol, atol=atol),
odespy.SymPy_odefun(problem),
odespy.ThetaRule(problem),
odespy.Trapezoidal(problem),
odespy.Vode(problem, rtol=rtol, atol=atol, adams_or_bdf=adams_or_bdf),
]