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*without* attempting to model any of the complicated underlying[lots of detail snipped]
dynamics of a real communicable disease epidemic, (which would
typically involve many coupled independent degrees of freedom, each
obeying their own mutually coupled ODEs, with frequent time dependent
updating of parameters of said degrees of freedom, and which would
have no closed form solution,
I consider a simple model for a cumulative sigmoidal growth process
with single dependent variable y for a temporal independent variable,
t, being the real line (or uniformly sampled real line) having the
following 4 aspects which need to be determined by the fitting
procedure.