Identification of Gumel-Mickens HIV model with incomplete information on a population

In this paper the Gumel-Mickens problem is considered, which includes a population of four types: HIV Susceptible, infected-vaccinated and infected- non vaccinated population and uninfected vaccinated population. It is assumed that data on the total population infected vaccinated and infected, and un-vaccinated population is available. It is shown that in this case of incomplete information it is possible to fully identify the mathematical model, i.e. find all coefficients of this model and restore information about HIV-suspected and uninfected vaccinated population.