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Prediction models based on different concepts have been proposed in recent years. The accuracy rates resulting from linear models such as exponential smoothing, linear regression (LR) and autoregressive integrated moving average (ARIMA) are not high as they are poor in handling the nonlinear relationships among the data. Neural network models are considered to be better in handling such nonlinear relationships. Healthcare time series data such as Morbidity of Tuberculosis (MTB) consist of complex linear and nonlinear patterns and it may be difficult to obtain high prediction accuracy rates using only linear or neural network models. Hybrid models which combine both linear and neural network models can be used to obtain high prediction accuracy rates. In this paper, we propose an adaptive hybrid algorithm to achieve the best results for time series prediction in healthcare. We also make a comparison of the proposed model with other known models based on accuracy rates.