Infectious disease prevention and control are important in improving, promoting and protecting the health of communities. Epidemiological data analysis plays a crucial role in disease prevention and control. Conventional methods such as moving average or autoregressive analysis normally require the assumption of stationarity, which is often violated in epidemiologic time series. This paper proposes the fusion of neural networks, fuzzy systems and genetic algorithms, with the aim to strengthen the modeling power for epidemiological dynamics. We deploy an additive fuzzy system into a neural network architecture in order to incorporate recurrent nodes to enable the fuzzy system to handle temporal data. The genetic algorithm is employed to optimize the fuzzy rule structure before supervised training is applied to adjust parameters. As epidemiological time series exhibit complex behavior and possibly cyclic patterns, the addition of recurrent nodes to the fuzzy system improves the modeling capability. The proposed model dominates the benchmark feedforward neural network and adaptive neuro-fuzzy inference system model regarding modeling performance. Through real applications for epidemiologic time series modeling, the fusion of soft computing techniques offer accurate forecasts that have considerable meaning in planning infectious disease-control activities.