RxSwift subject to provide public triggering but private subscription

Example.swift

class API {
    func obtainIds() -> Observable<[Int]> {
        return .just([1,2,3,4])
    }
}

class ViewModel {
    let update: AnyObserver<Void>
    let dataUpdated: Observable<[String]>

    init(api: API) {
        //
        // here is where we create the input/output
        let subject = PublishSubject<Void>()
        //
        //
        self.update = subject.asObserver()
        self.dataUpdated = subject.asObservable()
            .flatMap {
                return api
                    .obtainIds()
                    .catchErrorJustReturn([])
            }
            .map { $0.flatMap(String.init) }
    }
}

// in your view controllers data binding..
let viewModel = ViewModel(api: API())
// perhaps bind to a tableview
viewModel.dataUpdated.subscribe { e in
    print(e)
}
// button triggers the input
someButton.rx.tap.bind(to: viewModel.update)