from pylab import *
# In[11]:
from pyndamics import Simulation
from pyndamics.emcee import *
# ## 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]:
infected_data = np.array([1,2,5,6,7,8,9,11,13,15])
t_data=np.array([0,1,2,3,4,5,6,7,8,9])
# $$
# \frac{dS}{dt} = - \beta S I /N
# $$
#
# $$
# \frac{dI}{dt} = + \beta S I /N - \gamma I
# $$
# 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))
#
# Pyndamics provides a way to describe a dynamical system in terms of the differential equations, or the stock-flow formalism. It is a wrapper around the Scipy odeint function, with further functionality for time plots, phase plots, and vector fields.
#
# Page for this package: [https://code.google.com/p/pyndamics/](https://code.google.com/p/pyndamics/)
# In[1]:
from pyndamics import Simulation
# ## Population of Mice - Exponential Growth
#
# ### Specifying the Differential Equation
# In[2]:
sim = Simulation() # get a simulation object
sim.add(
"mice'=b*mice - d*mice", # the equations
100, # initial value
plot=True) # display a plot
sim.params(b=1.1, d=0.08)
sim.run(0, 4)
# fig=sim.figures[0]
# fig.savefig('mice.pdf')
# fig.savefig('mice.png')
# ### Specifying the Inflows/Outflows
