With the restrictions in our daily life activities under the current situation of the covid-19 pandemic worldwide, billions of people rely on social media platforms to share and obtaining covid-19 related news information. This made social media platforms easily be used as a source of myths and disinformation, which can cause severe public risks. It is thus of vital importance to constraint the spread of misinformation to the public. Although many works have shown promising results on the misinformation detection problem, only a few studies focus on the infodemic detection during the covid-19 pandemic, especially in the low resource language like Thai. Therefore, in this paper, we conduct extensive experiments on the real-world social network datasets to detect misinformation about covid-19 targeting both English and Thai languages. In particular, we perform an exploratory data analysis to get the statistic and characteristics of real and fake content. Also, we evaluate a series of three feature extraction, seven traditional machine learning, and eleven deep learning methods in detecting the fabricated content on social media platforms. The experimental results demonstrate that the transformer-based model significantly outperforms other deep learning and traditional machine learning methods in all metrics, including accuracy and F-measure.