AWS Supports "Pilot Light" style disaster recovery.
This is where part of the solution runs in AWS and is available to scale up if
needed for a failure.
Another approach is a full environment on standby as a hot failover.
In both scenarios, automation replication and connectivity changes to make
this happen are up to you.
There are 3rd party solutions that assist with automated DR.
https://aws.amazon.com/disaster-recovery/