if t >= tau:
return beta1 + (beta0 - beta1)**(-q * (t - tau))
else:
return beta0
# <codecell>
N = 1000000
sim = Simulation()
sim.add("S'=-beta(t)*(S*I)/N", N, plot=False)
sim.add("E'=-beta(t)*(S*I)/N - (E/invk)", 135, plot=1)
sim.add("I'=(E/invk) - (1/invGamma *I)", 136, plot=1)
sim.add("R'=(1/invGamma*I)", 0, plot=False)
sim.params(N=N, k=1 / 6.3, q=0.1000, invGamma=5.5000, invk=6.3)
sim.functions(beta)
sim.add_data(t=numOfDays, I=numOfCases, plot=1)
sim.run(0, 350)
# <codecell>
model = MCMCModel(
sim, {
'beta0': [0, 1],
'invGamma': [3.5, 10.7],
'beta1': [0, 1],
'q': [0, 100],
'tau': [100, 150],
'invk': [5, 22]
})
#model = MCMCModel(sim,{'invGamma':[3.5,10.7],'q':[0,10]})
# or you can define your own...
# <codecell>
def foo(y):
return tanh(y)
sim=Simulation() # get a simulation object
sim.add("x' = -x + foo(a*x)", # the equations
1, # initial value
plot=True) # display a plot
sim.params(a=2)
sim.functions(foo)
sim.run(0,40)
# <markdowncell>
# ## Alternate Integrators
#
# By default, pyndamics uses odeint, but you can also specify a few different intergrators. I have implemented euler, rk2, rk4, and rk45.
# <codecell>
from pyndamics import Simulation
sim=Simulation(method='rk45')
sim.add("deer' = r*deer*(1-deer/K)-c*deer*wolf",
initial_value=350,
from numpy import tanh
def foo(y):
return tanh(y)
sim = Simulation() # get a simulation object
sim.add(
"x' = -x + foo(a*x)", # the equations
1, # initial value
plot=True) # display a plot
sim.params(a=2)
sim.functions(foo)
sim.run(0, 40)
# ## Alternate Integrators
#
# By default, pyndamics uses odeint, but you can also specify a few different intergrators. I have implemented euler, rk2, rk4, and rk45.
# In[34]:
from pyndamics import Simulation
sim = Simulation(method='rk45')
sim.add("deer' = r*deer*(1-deer/K)-c*deer*wolf", initial_value=350, plot=True)
sim.add("wolf' = -Wd*wolf+D*deer*wolf", initial_value=50, plot=True)
