def test_Vector_State1(self):
# state is a vector
state_list = ['y1:4']
param_list = []
# transitions call from the vector
transition_list = [
Transition(origin='y[0]',
destination='y[1]',
equation='0.04*y[0]',
transition_type=TransitionType.T),
Transition(origin='y[1]',
destination='y[0]',
equation='1e4*y[1]*y[2]',
transition_type=TransitionType.T),
Transition(origin='y[1]',
destination='y[2]',
equation='3e7*y[1]*y[1]',
transition_type=TransitionType.T)
]
# initialize the model
ode = DeterministicOde(state_list, param_list,
transition=transition_list)
ode.get_ode_eqn()
t = numpy.append(0, 4*numpy.logspace(-6, 6, 1000))
ode.initial_values = ([1.0, 0.0, 0.0], t[0])
# try to integrate to see if there is any problem
_solution, _output = ode.integrate(t[1::], full_output=True)
def test_Vector_State3(self):
# state is a vector
state_list = [ODEVariable('y1', 'y1'),
ODEVariable('y2', 's'),
ODEVariable('y3', 'x')]
param_list = []
# transitions are explicit names
transition_list = [
Transition(origin='y1',
destination='y2',
equation='0.04*y1',
transition_type=TransitionType.T),
Transition(origin='y2',
destination='y1',
equation='1e4*y2*y3',
transition_type=TransitionType.T),
Transition(origin='y2',
destination='y3',
equation='3e7*y2*y2',
transition_type=TransitionType.T)
]
ode = DeterministicOde(state_list, param_list,
transition=transition_list)
ode.get_ode_eqn()
t = numpy.append(0, 4*numpy.logspace(-6, 6, 1000))
ode.initial_values = ([1.0, 0.0, 0.0], t[0])
# try to integrate to see if there is any problem
solution, output = ode.integrate(t[1::], full_output=True)
def test_deterministic(self):
ode = DeterministicOde(self.states,
self.params,
birth_death=self.birth_deaths,
transition=self.transitions)
ode.parameters = self.param_eval
ode.initial_values = (self.x0, self.t[0])
_solution = ode.integrate(self.t[1::])
def test_deterministic(self):
ode = DeterministicOde(self.states,
self.params,
birth_death=self.birth_deaths,
transition=self.transitions)
ode.parameters = self.param_eval
ode.initial_values = (self.x0, self.t[0])
_solution = ode.integrate(self.t[1::])
class TestSIRDiscreteEstimate(TestCase):
def setUp(self):
# initial values
N = 2362205.0
self.x0 = [N, 3.0, 0.0]
self.t = np.linspace(0, 150, 100).astype('float64')
# params
param_eval = [('beta', 0.5), ('gamma', 1.0 / 3.0), ('N', N)]
state_list = ['S', 'I', 'R']
param_list = ['beta', 'gamma', 'N']
transition_list = [
Transition(origin='S',
destination='I',
equation='beta * S * I/N',
transition_type=TransitionType.T),
Transition(origin='I',
destination='R',
equation='gamma * I',
transition_type=TransitionType.T)
]
# initialize the model
self.ode = DeterministicOde(state_list,
param_list,
transition=transition_list)
self.ode.parameters = param_eval
self.ode.initial_values = (self.x0, self.t[0])
# Standard. Find the solution.
self.solution = self.ode.integrate(self.t[1::])
# initial value
self.theta = np.array([0.4, 0.3])
# constraints
EPSILON = np.sqrt(np.finfo(np.float).eps)
self.box_bounds = [(EPSILON, 2), (EPSILON, 2)]
self.target = np.array([0.5, 1.0 / 3.0])
def test_SIR_Estimate_PoissonLoss_1TargetState(self):
obj = PoissonLoss(self.theta,
self.ode,
self.x0,
self.t[0],
self.t[1::],
np.round(self.solution[1::, 2]),
'R',
target_param=['beta', 'gamma'])
res = scipy.optimize.minimize(fun=obj.cost,
jac=obj.sensitivity,
x0=self.theta,
method='L-BFGS-B',
bounds=self.box_bounds)
self.assertTrue(np.allclose(res['x'], self.target))
def test_SIR_Estimate_PoissonLoss_2TargetState(self):
# note that we need to round the observations to integer for it
# to make sense
obj = PoissonLoss(self.theta,
self.ode,
self.x0,
self.t[0],
self.t[1::],
np.round(self.solution[1::, 1:3]), ['I', 'R'],
target_param=['beta', 'gamma'])
res = scipy.optimize.minimize(fun=obj.cost,
jac=obj.sensitivity,
x0=self.theta,
method='L-BFGS-B',
bounds=self.box_bounds)
self.assertTrue(np.allclose(res['x'], self.target))
'tau': 0.16,
'Rec_rate': 1.7,
'p': 0.2,
'beta': 0.371,
'mu': (1 / 63) / 365,
'eta': 0.7,
}
sierra_leone_parameters = {
'phi_H': 1.6,
'sigma_I': 0.1,
'sigma_H': 0.5,
'theta_I': 0.1,
'theta_H': 0.2,
'alpha': 0.1,
'tau': 0.16,
'Rec_rate': 1.7,
'p': 0.2,
'beta': 0.371,
'mu': (1 / 63) / 365,
'eta': 0.7,
}
model_system.parameters = liberia_parameters
solution, output = model_system.integrate(t[1::], full_output=True)
model_system.plot()
model_system.parameters = sierra_leone_parameters
solution, output = model_system.integrate(t[1::], full_output=True)
model_system.plot()