Modelling the HIV-AIDS Cuban Epidemics with Hopfield Neural Networks ⋆ M. Atencia 1 , G. Joya 2 , and F. Sandoval 2 1 Departamento de Matem´atica Aplicada. E.T.S.I.Inform´atica 2 Departamento de Tecnolog´ ıaElectr´onica.E.T.S.I.Telecomunicaci´ on Universidad de M´alaga, Campus de Teatinos, 29071 M´alaga, Spain matencia@ctima.uma.es Abstract. In this work, Hopfield neural networks are applied to estima- tion of parameters in a dynamical model of Cuban HIV-AIDS epidemics. The time-varying weights are derived, and its formulation is adapted to the discrete case. The method is tested on a data sequence obtained from numerical solution of the model. Simulation results show that the proposed technique quickly reduces the output prediction error, and it adapts well to parameter changes. Results concerning estimation error are poor, and some directions to deal with this issue are proposed. 1 Introduction System identification or modelling consists in the determination of the internal properties of a dynamical system, from some measurable external outputs. When no a priori information about the system exists, identification aims at building a model with the only information extracted from observed input-output data. This is an appropriate framework for techniques based upon statistical regres- sion, such as ARMAX and similar methods (see [1] and references therein). On the contrary, when a system model is available, either from physical laws or by our insight into the problem, it is logical not to waste the knowledge provided by the model. In this case, however, the knowledge is not complete, since the numerical value of some parameters of the model must be adjusted. Hence, this task is usually referred to as ”gray box” identification of a parametric model [2] or, simply, parameter estimation. The problem of parameter estimation is often addressed by the gradient method [3], which is an on-line estimator, i.e. it continuously modifies the esti- mation in the direction of error minimization. However, since the actual value of parameters is unknown, so is the estimation error. Hence, the only measure of the goodness of estimation is the output prediction error, i.e. the difference between the observed output and the predicted output. Consider a general ho- mogeneous dynamical system ˙ x = f (x, θ) where θ is a parameter vector. For ⋆ This work has been partially supported by the Spanish Ministerio de Ciencia y Tec- nolog´ ıa (MCYT), Project No. TIC2001-1758. Thanks are due to Hector de Arazoza for providing the model and Liuva Pedroso for generating test data.