  We consider a lognormal diffusion process having a multisigmoidal logistic
mean, useful to model the evolution of a population which reaches the maximum
level of the growth after many stages. Referring to the problem of statistical
inference, two procedures to find the maximum likelihood estimates of the
unknown parameters are described. One is based on the resolution of the system
of the critical points of the likelihood function, and the other is on the
maximization of the likelihood function with the simulated annealing algorithm.
A simulation study to validate the described strategies for finding the
estimates is also presented, with a real application to epidemiological data.
Special attention is also devoted to the first-passage-time problem of the
considered diffusion process through a fixed boundary.
