The description for a model is simply an attribute in the entity "Model Metadata Definition", that lives in the "Metadata" model. So changing the value should be just like changing the attribute value of any other entity.
Since I've never used the MDS API, I will describe how to do it using the MDS Stage Member tables and stored procedures, but I think this should give you an idea of how to do it using the API as well.
Since we're changing the "Description" attribute of member 22 (which is your Test-model), insert a record in the tblStgMemberAttribute-table:
insert mdm.tblStgMemberAttribute (ModelName, EntityName, MemberType_ID,
MemberCode, AttributeName, AttributeValue)
values ('Metadata', 'Model Metadata Definition', 1,
22, 'Description', 'My new description')
Then, you can either execute the batch using the manager, or execute it programmatically:
DECLARE @Version_ID int, @User_Id int
/* Get latest version of the model */
SET @Version_ID = (SELECT MAX(ID) FROM MDS.mdm.viw_SYSTEM_SCHEMA_VERSION
WHERE Model_Name = 'Metadata')
/* Get the UserID from the username */
SET @User_Id = (SELECT ID FROM mdm.tblUser u
WHERE u.UserName = 'domain\username') /* TODO: Replace domain/username */
EXEC mdm.udpStagingSweep @User_Id, @Version_ID, 1