In a statement here, Apollo Hospitals said that the treatment plan including appropriate antibiotics, respiratory support and other allied clinical measures are presently being continued to treat the infection.
It said that Jayalalithaa is "responding adequately to the comprehensive treatment being given to her" and she has been advised further stay in the hospital for treatment.
The 68-year-old Jayalalithaa was admitted to Apollo Hospital for fever and dehydration on September 22.
Subsequently, Apollo Hospital said she was cured of fever and needed to be in the hospital for observation.
In a statement on Sunday, Apollo Hospitals too said Jayalalithaa is responding well to the treatement given to her but has been advised a few more days stay in hospital.
It said that the current treatment plan is based on the detailed discussions the expert group of doctors had with British doctor Richard Beale, a consultant in Intensive Care Medicine at Guy's and St. Thomas Hospital, London.
As per the London hospital's website, Beale is one of its critical care consultants and clinical director, perioperative, pain and critical care directorate.
He is an experienced investigator in the fields of sepsis, ARDS, haemodynamics, critical care nutrition and ICU informatics.
Meanwhile, some AIADMK party men, braved the sun, to maintain a vigil outside the hospital.
They said they would be there till their leader Jayalalithaa gets well and discharged from the hospital.
Party men said that being outside the hospital helps them to know the real health condition of their leader and they need not get tense on baseless rumours spread in the social media.
The cadres also conduct special poojas.