Hi @Matt5 
Thank you for reaching out!
As it stands, there isn’t a feature to prevent other users to complete tasks that have been assign to you. There is a popular thread in the #productfeedback category regarding this topic: Asana User Permissions. If you haven’t yet, I would recommend you to have a look and upvote it.
As a workaround, you could create subtasks to interact with your colleagues. You can assign these subtasks to your colleagues and once they complete their part of the task, they can mark the subtask as complete but the parent task, assign to you, remains as incomplete.
I hope this helps @Matt5 