to + infinitive
This structure is used when the reported action aligns with the time of reporting.
- He is said to have the biggest private art collection in the country
- (implying it’s true now).
 
 - They were believed to be secretly in love
- (past belief about their current state).
 
 
Additionally, this structure can be used to make predictions about the future.
- She is expected to become a superstar
- (prediction based on current indications).
 
 
to + be -ing
This structure is used when the reported action is in progress simultaneously to the reporting.
- They are thought to be living under strict protection.
 
to + have participle
This structure is used when the reported action is previous to the reporting (earlier in the past)
- She was thought to have left the previous week.
- (she left before people thought about it)
 
 - He is claimed to have hit another student.
- (he hit another student first and people claimed he did it later)