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The particulate matter PM 10 concentrations have been impacting hospital admissions due to respiratory diseases. The air pollution studies seek to understand how this pollutant affects the health system. Since prediction involves several variables, any disparity causes a disturbance in the overall system, increasing the difficulty of the models' development. Due to the complex nonlinear behavior of the problem and their influencing factors, Artificial Neural Networks are attractive approaches for solving estimations problems. This paper explores two neural network architectures denoted unorganized machines: the echo state networks and the extreme learning machines. Beyond the standard forms, models variations are also proposed: the regularization parameter (RP) to increase the generalization capability, and the Volterra filter to explore nonlinear patterns of the hidden layers. To evaluate the proposed models' performance for the hospital admissions estimation by respiratory diseases, three cities of São Paulo state, Brazil: Cubatão, Campinas and São Paulo, are investigated. Numerical results show the standard models' superior performance for most scenarios. Nevertheless, considering divergent intensity in hospital admissions, the RP models present the best results in terms of data dispersion. Finally, an overall analysis highlights the models' efficiency to assist the hospital admissions management during high air pollution episodes. [ABSTRACT FROM AUTHOR]