While a 53-year-old woman from Chattarpur died at Ram Manohar Lohiya hospital, a 50-year-old woman from Patel Nagar passed away at Safdarjung hospital, officials said.
Also, 26 people tested positive for the virus, taking the number of cases to 199 this month.
"The two women tested positive for H1N1 virus and died during the course of treatment. Now the two cases are being reviewed to reconfirm that they died of swine flu," said R N Das, who is part of the five-member team constituted by the health department to review the cases.
Das maintained that there was no cause for alarm and the seasonal infection will disappear once warmer days set in.
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Samples are being sent to National Centre for Disease Control (NCDC) to confirm whether they are swine flu cases.
"We have enough medicines in stock. The 11 District Surveillance Officers nominated by the health department are checking that the 22 designated hospitals are following the standard operating procedures for treatment of swine flu," he said.
Swine influenza A (H1N1) virus spreads in the same way as the seasonal flu and even the symptoms are similar to the symptoms of regular flu which includes fever, cough, sore throat, body aches, headache, vomiting, diarrhoea, and fatigue.
"Infected people can pass the infection to others a day before symptoms develop and up to seven or more days after becoming sick," said a health expert.
However, it can be serious for elderly or children with low immunity or people who have health complications like heart diseases, cancer, HIV, diabetes or pregnant women, elderly or children with low immunity, he added.