  A stochastic diffusion process, whose mean function is a hyperbolastic curve
of type I, is presented. Themain characteristics of the process are studied and
the problem of maximum likelihood estimation forthe parameters of the process
is considered. To this end, the firefly metaheuristic optimization algo-rithm
is applied after bounding the parametric space by a stagewise procedure. Some
examples basedon simulated sample paths and real data illustrate this
development.
