Action (Activity) centered approach is a Qualified Relation Modeling Pattern [2]. This is suitable for modeling actions.
1. schema.org
http://schema.org/Action - http://schema.org/participant - http://schema.org/Person or Organization
http://schema.org/participant has many sub properties like http://schema.org/seller etc.
2. SIOC Action
3. Activity Streams
Activity - actor - Actor with Activity - target - Actor
Which is similar to schema.org approach, but without specifics the actor name (participant or seller). Which one is better? Activity already incorporates the activity context, then why schema.org needs to specify the actor?
If we would like to model result as well (join the group and become a member as a result), Role can be one of the options. Membership (as a subclass of Role) can have additional information like startDate and endDate
Current status then can be inferred by the logs or result, however, if the current status need to be explicitly described for simplicity or development needs, single property to indicate current status like (Person - member - Organization) which used most currently can be added as well.
REFERENCES
[1]. Activity Vocabulary
[2]. Qualified Relation
[3]. N-Ary