How are the menstrual cycle and prayer calculated for my wife, who has her period every week due to birth control pills, knowing that the actual date of her period is unknown?

If a woman's purity is interrupted, she should complete her regular cycle from the days of bleeding, then she is considered pure. If the bleeding returns before a complete period of purity (fifteen days), she should account for those days to complete her cycle, and anything beyond that is considered Istihada (non-menstrual bleeding). She continues this until the bleeding stops for fifteen consecutive days, or until a distinction in the blood appears. If the bleeding stops for this period or she distinguishes it after fifteen days of Istihada, it becomes a new menstruation.