When COVID-19 first emerged, it was assumed that the virus induces only lung disease, but more and more studies have shown that the whole body gets affected. While the exact number is unclear (reports vary from 3% - 79% of patients), many COVID-19 patients experience gastrointestinal symptoms. The most common gastrointestinal symptoms are anorexia and diarrhea.
A few patients (one study reported 6 cases) even showed digestive symptoms without any respiratory symptoms. The number of patients with atypical symptoms could be higher, but those cases stay most likely undetected. 
One study found that the ratio of chronic liver disease was higher in patients with COVID-19 with gastrointestinal symptoms, which leads to increased levels of ALT and AST. The cause of this correlation is still unknown. 
It is difficult to determine - especially in severe COVID-19 cases - whether gastrointestinal symptoms are direct consequences of viral infection or secondary symptoms due to inflammatory reactions within the body or side effects of drugs that are used for treatment. 
However, recent findings suggest direct gastrointestinal infection with SARS-CoV-2. Angiotensin-converting enzyme (ACE) 2, the protein used by SARS-CoV-2 as a viral receptor for cell-entry, is highly expressed in the gastrointestinal tract. Immunofluorescent data showed high amounts of ACE2 in the glandular cells of gastric, duodenal, and rectal epithelia, supporting the theory of direct viral infection of gastrointestinal cells.  Additionally, the protein shell of the virus was found in gastric, duodenal, and rectal cells, which suggests virus replication in the gastrointestinal tract. 
Viral RNA was also detected in feces. It is still unclear whether the virus in feces is intact and infectious, or if only viral RNA and proteins remain. In case the virus in stool stays infectious, fecal-oral transmission could be a potential risk. Studies showed that toilet bowls and sink samples were positive for SARS-CoV-2 RNA. Fecal-oral transmission could occur when individuals touch their mouth, nose, or eyes with contaminated hands. 
In one study, more than 20% of patients showed positive results for viral RNA in feces, even after viral RNA in the respiratory tract was cleared. These findings indicate the potential for fecal-oral transmission to occur for a more extended period than respiratory transmission. 
Fecal-oral transmission could be an undetected issue. In this case, testing of viral RNA in feces might become clinically significant, not just for identification of undetected COVID-19 patients, but also to control the chain of transmission.
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- Lamers M., et al. "SARS-CoV-2 productively infects human gut enterocytes." Science (2020).
- Xiao F, et al. "Evidence for gastrointestinal infection of SARS-CoV-2." Gastroenterology 158.6 (2020): 1831-1833.
- Ong, Sean Wei Xiang, et al. "Air, surface environmental, and personal protective equipment contamination by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) from a symptomatic patient." Jama 323.16 (2020): 1610-1612.