An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China

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In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO–NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt–Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt–Winters exponential smoothing method.