The COVID-19 epidemic has swept the world for over a year. However, a large number of infectious asymptomatic COVID-19 cases (\textit{ACC}s) are still making the breaking up of the transmission chains very difficult. Efforts by epidemiological researchers in many countries have thrown light on the clinical features of ACCs, but there is still a lack of practical approaches to detect ACCs so as to help contain the pandemic. To address the issue of ACCs, this paper presents a neural network model called Spatio-Temporal Episodic Memory for COVID-19 (\textit{STEM-COVID}) to identify ACCs from contact tracing data. Based on the fusion Adaptive Resonance Theory (\textit{ART}), the model encodes a collective spatio-temporal episodic memory of individuals and incorporates an effective mechanism of parallel searches for ACCs. Specifically, the episodic traces of the identified positive cases are used to map out the episodic traces of suspected ACCs using a weighted evidence pooling method. To evaluate the efficacy of STEM-COVID, a realistic agent based simulation model for COVID-19 spreading is implemented based on the recent epidemiological findings on ACCs. The experiments based on rigorous simulation scenarios, manifesting the current situation of COVID-19 spread, show that the STEM-COVID model with weighted evidence pooling has a higher level of accuracy and efficiency for identifying ACCs when compared with several baselines. Moreover, the model displays strong robustness against noisy data and different ACC proportions, which partially reflects the effect of breakthrough infections after vaccination on the virus transmission.