While many conspiracy theories and fake news have spread about this, there is no evidence to suggest that Trump is faking his illness.
Michael Moore, a documentarian, circulated a post saying Trump is faking having COVID-19. According to him, Trump is trying to gain sympathy and earn votes from the public. QAnon peddled the theory that Trump's tweet on his wife and he is coronavirus positive has a secret message about getting Hillary Clinton arrested. Some say he is trying to boost hydroxychloroquine (HCQs) sales. Another tweet predicts that in 14 days, Trump will come out announcing he has been cured using HCQs.
Gideon Blocq, the CEO of VineSight, informed people that most of this information is spreading via unverified accounts on twitter.
Facebook has also started combating fake news and flagging it.
Different researchers who study the effect of misinformation and specialize in disinformation call this both a political crisis and a health crisis period. Online disinformation spreads fast following significant, breaking news events.
The COVID-19 pandemic has given rise to a lot of potentially dangerous misinformation. For reliable advice on COVID-19 including symptoms, prevention and available treatment, please refer to the World Health Organisation or your national healthcare authority.