The error is likely cause by the exponential of large value, check the logistic function:
x0=.5
k=500
t=np.linspace(0., 1., 2500)
np.exp(-k*(t-x0))
Out[38]:
array([3.74645461e+108, 3.06709213e+108, 2.51092169e+108, ...,
3.98260131e-109, 3.26041722e-109, 2.66919022e-109])
As you can see, the output is in a wildly large range. You should find a way to scale the parameter k.