Answer:
The method is known as systematic desensitization therapy, and incorporates in vivo exposure.
Explanation:
The systematic desensitization therapy it's a behavior therapy that was first applied by Dr. Joseph Wolpe, a South African psychiatrist as a way to deal with people's phobias.
The first step is learning relaxation and breathing techniques, which may include meditation.
Then a fear hierarchy is created as stated in your question. The patient goes on a scale from least feared scenarios, such as thinking about the feared object/animal, to the most feared scenarios, such as physical contact.
In Vivo exposure, means that the patient will be directly exposed to the object of his/her phobia. It is the opposite of In Vitro exposure, in which the patient will only imagine the phobic stimulus, and there is no direct contact or exposure.