Security and privacy

Well, Moodle is aimed for collaborative learning, so...

Anyway you can choose to use only the News forum, were students can't start new discussions, but only reply to discussions started by teachers. But this will not prevent students from communicate, they will be able to (mis)use the tread for their own purpose.

Then students can still communicate using messages. If you want to disable that too you have to set the capability "Send messages to any user" to "prevent" for authenticated users on the page
Administration > Users > Permissions > Define roles

This will prevent all your users to send messages to one another. If you only prevent students to send messages, they - if they are not having the role student sidewide - will be able to use the messaging system outside a course.

So if you want teachers still to be able to send messages you will have to allow the capability for teachers. But then students still can not send messages to teachers.

Hope this makes sense (and that I have understood it right myself), otherwise come back and ask again.