Jan 29 is labelled as the 11th day.
But Jan 23/24 was when the quarantine started and public awareness became widespread.
These measures should have sharply reduced the infectivity rate.
So the algorithm should really start at Jan 24.
not sure why you appear to insist on Jan 24, anyway I tabulate
a/(exp(-k*(DAY - xc))*(d - 1) + 1)^(1/(d - 1))
(coefficient values are in
Today at 1:30 PM graph)
from DAY #5 = Jan 24
day#5 440 confirmed cases, back-calculated: 1598
day#6 571 confirmed cases, back-calculated: 2008
day#7 830 confirmed cases, back-calculated: 2523
day#8 1287 confirmed cases, back-calculated: 3168
day#9 2744 confirmed cases, back-calculated: 3974
day#10 4515 confirmed cases, back-calculated: 4976
day#11 6061 confirmed cases, fitted: 6218
day#12 7771 confirmed cases, fitted: 7745
day#13 9692 confirmed cases, fitted: 9604
day#14 11943 confirmed cases, fitted: 11838
day#15 14562 confirmed cases, fitted: 14469
day#16 17383 confirmed cases, fitted: 17492
day#17 20624 confirmed cases, fitted: 20853
day#18 24539 confirmed cases, fitted: 24440
day#19 28262 confirmed cases, fitted: 28089
day#20 31453 confirmed cases, fitted: 31605
day#21 34876 confirmed cases, fitted: 34810
day#22 37552 confirmed cases, fitted: 37574
23th day = Feb10: 39842 extrapolated from the fit
24th day = Feb11: 41625 extrapolated from the fit
25th day = Feb12: 42978 extrapolated from the fit
26th day = Feb13: 43977 extrapolated from the fit
27th day = Feb14: 44699 extrapolated from the fit
28th day = Feb15: 45214 extrapolated from the fit
29th day = Feb16: 45577 extrapolated from the fit
30th day = Feb17: 45830 extrapolated from the fit
31th day = Feb18: 46006 extrapolated from the fit
the top asymptote is 46399 (standard error of 1690) EDIT if the virus begins to spread from new sources, this model will become useless as a matter of course