An "aggregate root domain model which will have NO analogical database entity and will not be persisted in the database" is not a "fictitious aggregate"; it is a standard aggregate just like another aggregate that it needs to be persisted. The purpose of an aggregate is to control the changes following domain rules to ensure consistency and invariants.
Sometimes the aggregate is the change (and need to be persisted) but sometimes it is not and the things to be persisted after the change are parts/full entities and/or VOs that changed inside the aggregate and are mapped in persistence at its own without the needed of composing a persistence concept (table/s, document, etc). This is a implementation detail about how you decided to persist your domain data.
First premise of DDD: There is no DataBase. This helps you to not think too biased about trying to mapping persistence concepts in your domain.
Mike in his blog explain it better than me.
The purpose of our aggregate is to control change, not be the change.
Yes, we have data there organized as Value Objects or Entity
references but that’s because it’s the easiest and most maintainable
way to enforce the business rules. We’re not interested in the state
itself, we’re interested in ensuring that the intended changes respect
the rules and for that we’re ‘borrowing’ the domain mindset i.e we
look at things as if WE were part of the business.
An aggregate instance communicates that everything is ok for a
specific business state change to happen. And, yes, we need to persist
the busines state changes. But that doesn’t mean the aggregate itself
needs to be persisted (a possible implementation detail). Remember
that the aggregate is just a construct to organize business rules,
it’s not a meant to be a representation of state.
So, if the aggregate is not the change itself, what is it? The change
is expressed as one or more relevant Domain Events that are generated
by the aggregate. And those need to be recorded (persisted) and
applied (interpreted). When we apply an event we “process” the
business implications of it. This means some value has changed or a
business scenario can be triggered.