from scipy.optimize import curve_fit
import numpy as np

def sigmoid(x, x0, k):
y = 1 / (1 + np.exp(-k*(x-x0)))
return y

ppov, pcov = curve_fit(sigmoid, np.arange(len(ydata)), ydata, maxfev=20000)

ydata1 = [0,0,0,0,0,91,91]

RuntimeError: Optimal parameters not found: gtol=0.000000 is too small func(x) is orthogonal to the columns of the Jacobian to machine precision.

ppov, pcov = curve_fit(sigmoid, np.arange(len(ydata1)), ydata1, maxfev=20000, method='dogbox')
print(ppov[0], ppov[1])
5.189237217957538 11.509279446215949

ydata2=[0,3,5,30,34,50,91]

ppov, pcov = curve_fit(sigmoid, np.arange(len(ydata2)), ydata2, maxfev=20000)
print(ppov[0], ppov[1])
-24.681668846480264 118.77183210605865

ppov, pcov = curve_fit(sigmoid, np.arange(len(ydata2)), ydata2,  maxfev=20000, method='dogbox')
print(ppov[0], ppov[1])
0.28468096463676695 8.154477352500013