Dernbach and Meaker were granted compassionate leave to travel to Wales on Wednesday for the funeral of former Surrey batsman Tom Maynard, who died after being hit by an underground train on June 17. He was 23.
Meaker was originally summoned as a replacement for James Anderson, who missed Sunday's win in the second ODI with a groin injury but is hoping to be fit for the final three matches in the series.
England has a 2-0 lead and can wrap up the series by beating the tourists at Edgbaston on Wednesday.