While many conspiracy theories and fake news has been spreading related to 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 the votes from the public. QAnon peddled the theory that Trump's tweet on his wife and he is positive has a secret message relating to 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 spread 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 calls this both a political crisis weeks before the election and a health crisis period. Online disinformation spreads fast following significant, breaking news events - and this is no exception for it.
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.