次のページを参考にしました。
python - OptimizeWarningを例外としてキャッチする

curve_fit02.py

# ! /usr/bin/python
#
import sys
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

import warnings
from scipy.optimize import OptimizeWarning

warnings.simplefilter("error", OptimizeWarning)
# ------------------------------------------------------------------
def exp(xx, aa, bb, dd, pp):
	rvalue = 0.0
	try:
		rvalue = dd * np.exp(aa * xx - bb) + pp
	except Exception as ee:
		sys.stderr.write("*** error *** in exp ***\n")
		sys.stderr.write(str(ee) + "\n")
	return rvalue
# ------------------------------------------------------------------
xx = np.array([0,1,2,3,4,5])
yy = np.array([195.0, 200.0, 224.0,254.0, 298.0,345.0])
yy = np.array([195.0, 203.0, 224.0,254.0, 298.0,345.0])

popt = np.array([0.0,0.0,0.0,0.0])
print(type(popt))
    
try:
	popt, pcov = curve_fit(exp, xx, yy)
	print(popt)
	print(type(popt))
except Exception as ee:
	sys.stderr.write("*** error *** in curve_fit ***\n")
	sys.stderr.write(str(ee) + "\n")
    
plt.figure()
plt.plot(xx, yy, 'ko', label="Original Data")
plt.plot(xx,exp(xx, *popt), 'r-',label="Fitted Curve")
plt.legend()
plt.show()
# ------------------------------------------------------------------

次のメッセージが出ます。

<class 'numpy.ndarray'>
*** error *** in curve_fit ***
Covariance of the parameters could not be estimated