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Bayesian Optimization algorithm has become a promising approach for nonlinear global optimization problems and many machine learning applications. Over the past few years, improvements and enhancements have been brought forward and they have shown some promising results in solving the complex dynamic problems, systems of ordinary differential equations where the objective functions are computationally expensive to evaluate. Besides, the straightforward implementation of the Bayesian Optimization algorithm performs well merely for optimization problems with 10-20 dimensions. The study presented in this paper proposes a new high dimensional Bayesian Optimization algorithm combining Recurrent neural networks, which is expected to predict the optimal solution for the global optimization problems with high dimensional or time series decision models. The proposed RNN-BO algorithm can solve the optimal control problems in the lower dimension space and then learn from the historical data using the recurrent neural network to learn the historical optimal solution data and predict the optimal control strategy for any new initial system value setting. In addition, accurately and quickly providing the optimal control strategy is essential to effectively and efficiently control the epidemic spread while minimizing the associated financial costs. Therefore, to verify the effectiveness of the proposed algorithm, computational experiments are carried out on a deterministic SEIR epidemic model and a stochastic SIS optimal control model. Finally, we also discuss the impacts of different numbers of the RNN layers and training epochs on the trade-off between solution quality and related computational efforts.