One death was reported from East Champaran district two days ago.
Chief Minister Nitish Kumar - who had visited the town on Tuesday and issued elaborate instructions to tackle the situation - is scheduled to hold a high-level meeting in Gaya later in the day.
Infected patients were sharing beds in crowded hospital wards with too few doctors, while families who could afford it transferred their children to private hospitals in Patna and other larger cities.
Additional Collector of Cuttack, Srikant Tarai, said, "We are taking all the precautionary measures as per the direction of the Health Department".
Apart from 2014 when a record 357 children died in the state, the annual death toll is usually much lower.
The total number of AES cases registered since June 1 was 398 at the SKMCH and 154 at Kejriwal hospital, according to figures provided by the district administration.More news: Mats Hummels leaves Bayern Munich for Borussia Dortmund again
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The National Human Rights Commission has asked Prime Minister Narendra Modi's government and Kumar state authorities to report any "possible flaw" in implementation of vaccination and awareness programmes.
Young children are particularly vulnerable to the illness, which can cause swelling of the brain, fever and vomiting.
Between 2008 and 2014, there were more than 44,000 cases and almost 6,000 deaths due to encephalitis in India, particularly in Uttar Pradesh and Bihar. Sometime back, Gorakhpur district of Uttar Pradesh suffered a lot due to Japanese Encephalitis when about 60 children lost their lives.
Bihar Chief Secy Deepak Kumar said that the doctors are carrying out their duties but the chief minister has ordered to bring some doctors from Dharbhanga Medical College and Hospital and Patna Medical College and Hospital in order to help them.
Earlier Union Health Minister had visited the state to take stock of the situation and review measures taken in the wake of the outbreak.