Identication 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. nd
all coecients of this model  and restore information about HIV-suspected
and uninfected vaccinated population.
R. E. Mickens, K. Oyedeji, and S. Rucker, Exact finite difference scheme for second-order, linear ODEs having constant coecients, Journal of Sound and Vibration 287 1052-1056, 2005.
E. Gonzalez, H. Kulkarni, H. Bolivar, A. Mangano, R. Sanchez, G. Catano, R.J. Nibbs, B.I. Freedman, M.P. Quinones, M.J. Bamshad, and K.K. Murthy, The infuence of CCL3L1 gene-containing segmental duplications on HIV-1/AIDS susceptibility, Science 307 1434-1440, 2005.
V. DeGruttola, N. Lange, U. and Dafni, Modeling the progression of HIV infection, Journal of the American Statistical Association 86 569-577, 1991.
G. Maldonado, and S. Greenland, Interpreting model coefficients when the true model form is unknown, Epidemiology 1 310-318, 1993.