Modelling the HIV-AIDS Cuban Epidemics with Hopfield Neural Networks

In this work, Hopfield neural networks are applied to estimation 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]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[2]  Gonzalo Joya,et al.  Hopfield neural networks for optimization: study of the different dynamics , 2002 .

[3]  Heinz Unbehauen Some new trends in identification and modeling of nonlinear dynamical systems , 1996 .

[4]  N. Ling The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[5]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[6]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Gonzalo Joya,et al.  Gray box identification with hopfield neural networks , 2004 .

[8]  S. Abe Theories on the Hopfield neural networks , 1989, International 1989 Joint Conference on Neural Networks.

[9]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[10]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[11]  H. Arazoza,et al.  A non-linear model for a sexually transmitted disease with contact tracing. , 2002, IMA journal of mathematics applied in medicine and biology.

[12]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .