At this moment Epesi 1.8.2 runs on PHP up to 7.0 but I am running it also on 7.1 and 7.2. However there are compatibility problems reported by users and I also experienced some forcing me in some cases to downgrade to 7.0
In some environments like cpanel you can run 7.0 and 7.1 and 7.2 at the same time. The only problem is when a hosting provider decides to stop supporting 7.0. To address this issue we are preparing a long overdue release 1.9.0 which should be available 09/2019 to the public.
Version 1.9.0 will be compatible with PHP version 7.2 at least and possibly even 7.3