# In[6]:
from pyndamics import Simulation
from pyndamics.emcee import *
# In[7]:
t=array([7,14,21,28,35,42,49,56,63,70,77,84],float)
h=array([17.93,36.36,67.76,98.10,131,169.5,205.5,228.3,247.1,250.5,253.8,254.5])
sim=Simulation()
sim.add("h'=a*h*(1-h/K)",1,plot=True)
sim.add_data(t=t,h=h,plot=True)
sim.params(a=1,K=500)
sim.run(0,90)
# fig=sim.figures[0]
# fig.savefig('sunflower_logistic1.pdf')
# fig.savefig('sunflower_logistic1.png')
# In[8]:
model=MCMCModel(sim,
a=Uniform(.001,5),
K=Uniform(100,500),
initial_h=Uniform(0,100),
)
# \frac{dS}{dt} = - \beta S I /N
# $$
#
# $$
# \frac{dI}{dt} = + \beta S I /N - \gamma I
# $$
# In[22]:
sim=Simulation()
sim.add("N=S+I+R")
sim.add(" S' = -β*S*I/N",1000)
sim.add(" I' = +β*S*I/N - γ*I",1)
sim.add(" R' = +γ*I",0)
sim.add_data(t=t_data,S=susceptible_data)
sim.add_data(t=t_data,I=infected_data)
sim.params(β=0.3,γ=0.1)
sim.run(0,10)
# In[23]:
figure(figsize=(8,4))
t,S,I=sim.t,sim.S,sim.I
subplot(2,1,1)
plot(t,S,'-') # models plotted with solid line
plot(t_data,susceptible_data,'o') # data with markers
64.06406406, 68.06806807, 72.07207207, 76.07607608
]),
array([
-16.52420711, 0.83399691, 26.29032381, 92.46966588,
192.82511069, 360.21219894, 472.59465177, 516.91547329,
480.05384666, 463.98953003, 501.72818401, 456.0508904,
468.98941972, 512.73730732, 479.49668258, 483.76056329,
466.88367256, 501.29703993, 501.26889691, 486.47837681
]))
# In[24]:
sim = Simulation()
sim.add("y'=r*y*(1-y/K)", 1)
sim.params(r=1, K=200)
sim.add_data(t=x_data, y=y_data)
sim.run(0, 80)
# In[25]:
x = sim.t
y = sim.y
plot(x, y, 'b-')
plot(x_data, y_data, 'bo')
# ### make a statistical model and fit with MCMC...may take a while (2-5 min) to run when you do the run_mcmc line
# In[26]:
model = MCMCModel(sim, r=Uniform(0, 1), K=Uniform(300, 700))
plot(t, h, '-o')
xlabel('Days')
ylabel('Height [cm]')
# <markdowncell>
# ### Run an initial simulation
#
# Here, the constant value ($a=1$) is hand-picked, and doesn't fit the data particularly well.
# <codecell>
sim = Simulation()
sim.add("h'=a", 1, plot=True)
sim.add_data(t=t, h=h, plot=True)
sim.params(a=1)
sim.run(0, 12)
# <markdowncell>
# ### Fit the model parameter, $a$
#
# Specifying the prior probability distribution for $a$ as uniform between -10 and 10.
# <codecell>
model = MCMCModel(sim, {'a': [-10, 10]})
model.fit(iter=25000)
# <markdowncell>
44.54454454, 46.3963964 , 46.996997 , 47.2972973 ,
48.14814815, 48.74874875]),
array([ 1.14606519, 0.78658793, 0.15507708, 0.64491796, 0.3834882 ,
-0.65511548, -0.89478528, -0.24951861, 1.06321321, -0.04609502,
0.34452878, -0.18088143, -0.44538382, -0.72407121, -1.16075082,
-0.45408912, 0.95732637, 0.83271397, 0.20881338, -0.03971536,
-0.1518789 , -0.78984006, -0.83559018, -1.32878715, -0.99501354,
-0.74628129, -0.24701692, -0.03410385, 0.95727806, 1.07165818]))
# In[43]:
sim=Simulation()
sim.add("M'=1/(1+E)-alpha",1,plot=True)
sim.add("E'=M-beta",1,plot=True)
sim.add_data(t=t_data,M=M_data,plot=True)
sim.params(alpha=.4,beta=0.04)
sim.run(0,50)
# In[45]:
model=MCMCModel(sim,
alpha=Uniform(0,5),
beta=Uniform(0,5))
model.run_mcmc(500)
# In[46]:
model.plot_chains()
# In[3]:
t=array([1,2,2.5,3,3.5,4,4.5,5.5,6,7.5,8.5,10.5])
y=array([50.6,47.3,45.8,43.9,42.2,40.4,38.3,35,33.5,29,26.3,21.6])
plot(t,y,'-o')
# In[5]:
sim=Simulation()
sim.add("θ' = -Z*θ",53,plot=True)
sim.params(Z=1)
sim.add_data(t=t,θ=y,plot=True)
sim.run(0,11)
# In[ ]:
# In[8]:
sim=Simulation()
sim.add("θ' = -Z*θ",53,plot=True)
sim.params(Z=.01)
from pyndamics.emcee import *
# <markdowncell>
# ## Artificial Example with Mice Population
# <codecell>
data_t = [0, 1, 2, 3]
data_mouse = [2, 5, 7, 19]
sim = Simulation() # get a simulation object
sim.add("mice'=b*mice - d*mice", 2, plot=True) # the equations # initial value # display a plot, which is the default
sim.add_data(t=data_t, mice=data_mouse, plot=True)
sim.params(b=1.1, d=0.08) # specify the parameters
sim.run(5)
# <codecell>
model = MCMCModel(sim, b=Uniform(0, 10))
# <codecell>
model.set_initial_values()
model.plot_chains()
# <codecell>
model.run_mcmc(500)
# ## Artificial Example with Mice Population
# In[12]:
data_t = [0, 1, 2, 3]
data_mouse = [2, 5, 7, 19]
sim = Simulation() # get a simulation object
sim.add(
"mice'=b*mice - d*mice", # the equations
2, # initial value
plot=True) # display a plot, which is the default
sim.add_data(t=data_t, mice=data_mouse, plot=True)
sim.params(b=1.1, d=0.08) # specify the parameters
sim.run(5)
# In[13]:
model = MCMCModel(sim, b=Uniform(0, 10))
# In[14]:
model.set_initial_values()
model.plot_chains()
# In[15]:
model.run_mcmc(500)
# ## Artificial Example with Mice Population
# <codecell>
data_t = [0, 1, 2, 3]
data_mouse = [2, 5, 7, 19]
sim = Simulation() # get a simulation object
sim.add(
"mice'=b*mice - d*mice", # the equations
2, # initial value
plot=True) # display a plot, which is the default
sim.add_data(t=data_t, mice=data_mouse, plot=True)
sim.params(b=1.1, d=0.08) # specify the parameters
sim.run(5)
# <codecell>
model = MCMCModel(sim, {'b': [0, 10]})
model.fit(iter=25000)
# <codecell>
model.b
# <codecell>
sim.run(5)
# ## adding some data
# In[31]:
t_data = array([7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84], float)
h_data = array([
17.93, 36.36, 67.76, 98.10, 131, 169.5, 205.5, 228.3, 247.1, 250.5, 253.8,
254.5
])
sim = Simulation()
sim.figsize = (6, 4)
sim.add(" y'=r*y*(1-y/K) ", 1, plot=True)
sim.params(r=.2, K=270)
sim.add_data(t=t_data, y=h_data, plot=True)
sim.run(0, 100)
# In[35]:
model = MCMCModel(sim, r=Uniform(0, 1), K=Uniform(100, 400))
# In[36]:
model.run_mcmc(500)
# In[37]:
model.plot_chains()
# In[38]:
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]})
model.fit(iter=500)
1.14606519, 0.78658793, 0.15507708, 0.64491796,
0.3834882, -0.65511548, -0.89478528, -0.24951861,
1.06321321, -0.04609502, 0.34452878, -0.18088143,
-0.44538382, -0.72407121, -1.16075082, -0.45408912,
0.95732637, 0.83271397, 0.20881338, -0.03971536,
-0.1518789, -0.78984006, -0.83559018, -1.32878715,
-0.99501354, -0.74628129, -0.24701692, -0.03410385,
0.95727806, 1.07165818
]))
# In[43]:
sim = Simulation()
sim.add("M'=1/(1+E)-alpha", 1, plot=True)
sim.add("E'=M-beta", 1, plot=True)
sim.add_data(t=t_data, M=M_data, plot=True)
sim.params(alpha=.4, beta=0.04)
sim.run(0, 50)
# In[45]:
model = MCMCModel(sim, alpha=Uniform(0, 5), beta=Uniform(0, 5))
model.run_mcmc(500)
# In[46]:
model.plot_chains()
# In[49]:
model.set_initial_values('samples')
t = t[(t >= 2017.5) & (t <= 2018.5)]
t = (t - t[0]) * 365.25
# In[18]:
plot(t, y, '-o')
# In[19]:
sim = Simulation()
sim.add("N=S+I+R")
sim.add(" S' = -β*S*I/N", 3e8)
sim.add(" I' = +β*S*I/N - γ*I", 1, plot=True)
sim.add(" R' = +γ*I", 0)
sim.add_data(t=t, I=y, plot=True)
sim.params(β=0.3, γ=0.1)
sim.run(0, 365)
# In[27]:
sim = Simulation()
sim.add("N=S+I+R")
sim.add(" S' = -β*S*I/N", 3e8)
sim.add(" I' = +β*S*I/N - γ*I", 1, plot=True)
sim.add(" R' = +γ*I", 0)
sim.add_data(t=t, I=y, plot=True)
sim.params(β=0.08, γ=0.06)
sim.run(0, 365)
# In[29]:
