Currently Eritrea has no Vice President, so it appears that Woldemichael Abraha, the Minister of Local Government, would run the government.
Even if he was to take over as head of state it would not necessarily mean that he held the real power.
There are few references to Woldemichael Abraha, but he is quoted as having played an important role in the Ethiopian assault on the town of Nakfa in 1979 (see below).
Having participated in such a critical battle would be important in Eritrea, which still looks to its fight for independence as among its greatest achievement.
Source : Eritrea Hub