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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Birth-Death
This is for an integrated test of E-Cell4. Here, we test a simple birth-death process in volume.
Step1:  Parameters are given as follows. D and radius mean a diffusion constant and a radius of molecules, respectively. Dimensions of length and time are assumed to be micro-meter and second.
Step2:  Make a model for all algorithms. No birth reaction with more than one product is accepted.
Step3:  Save a result with ode as obs, and plot it
Step4:  Simulating with gillespie (Bars represent standard error of the mean)
Step5:  Simulating with meso
Step6:  Simulating with spatiocyte
Step7:  Simulating with egfrd
Step8:  Simulating with bd
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Python Code:
%matplotlib inline
from ecell4.prelude import *
Explanation: Birth-Death
This is for an integrated test of E-Cell4. Here, we test a simple birth-death process in volume.
End of explanation
D = 1  # 0.01
radius = 0.005
N = 20  # a number of samples
y0 = {} # {'A': 60}
duration = 3
V = 8
Explanation: Parameters are given as follows. D and radius mean a diffusion constant and a radius of molecules, respectively. Dimensions of length and time are assumed to be micro-meter and second.
End of explanation
with species_attributes():
    A | {'radius': radius, 'D': D}
with reaction_rules():
    ~A > A | 45.0
    A > ~A | 1.5
m = get_model()
Explanation: Make a model for all algorithms. No birth reaction with more than one product is accepted.
End of explanation
ret1 = run_simulation(duration, y0=y0, volume=V, model=m)
ret1
Explanation: Save a result with ode as obs, and plot it:
End of explanation
ret2 = ensemble_simulations(duration, ndiv=20, y0=y0, volume=V, model=m, solver='gillespie', repeat=N)
ret2.plot('o', ret1, '-')
Explanation: Simulating with gillespie (Bars represent standard error of the mean):
End of explanation
ret2 = ensemble_simulations(
    duration, ndiv=20, y0=y0, volume=V, model=m, solver=('meso', Integer3(3, 3, 3), 0.25), repeat=N)
ret2.plot('o', ret1, '-')
Explanation: Simulating with meso:
End of explanation
ret2 = ensemble_simulations(
    duration, ndiv=20, y0=y0, volume=V, model=m, solver=('spatiocyte', radius), repeat=N)
ret2.plot('o', ret1, '-')
Explanation: Simulating with spatiocyte:
End of explanation
ret2 = ensemble_simulations(
    duration, ndiv=20, y0=y0, volume=V, model=m, solver=('egfrd', Integer3(8, 8, 8)), repeat=N)
ret2.plot('o', ret1, '-')
Explanation: Simulating with egfrd:
End of explanation
ret2 = ensemble_simulations(
    duration, ndiv=20, y0=y0, volume=V, model=m, solver=('bd', Integer3(8, 8, 8), 0.1), repeat=N)
ret2.plot('o', ret1, '-')
Explanation: Simulating with bd:
End of explanation
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