This article develops an EM (expectation-maximisation) algorithm and related computationally intensive procedures for iterative estimation of the HIV infection rates and prediction of the future course of AIDS incidence in Canada, U.S. and Australia.. First, likelihood functions are constructed by assuming nonhomogeneous Poisson and planar Poisson point processes for infections and incidences. Smooth maximum likelihood estimates of the HIV infection rates are then obtained by applying the EM algorithm coupled with a smoothing step at each iteration. Accuracy of the estimates of the infection rates can then be checked by comparing the estimates of the expected AIDS incidence, calculated from the Volterra integral equation of the first kind using the known incubation distribution as the kernel. Furthermore, by extrapolating the estimates of the HIV infection rates so obtained into the future, the Volterra integral equation can be used to project the future course of the AIDS incidence. We have employed various parametric and nonparametric distributions for the kernel. The parametric distributions include Weibull and gamma distributions and several new distribution functions and the non-parametric distributions include linear and cubic spline functions. These are so chosen as to take into account the fact that the HIV screening test was available in these countries only since 1985 and the drug treatment made available to the HIV positive patients only after 1987. Our method has produced results that fit the observed AIDS incidence better than those produced by other existing methods based on data from U.S., Canada and Australia.