Dr Constantine was a physician working in Albion Hospital when it was overrun by the Empty Child plague. Constantine was the last person in the hospital unaffected by the nanogenes. He led the Ninth Doctor to the first elements of understanding the plague.
Dr Constantine worked at Albion hospital during the Blitz, but in early 1941, Constantine showed signs of an illness and apparently believed he was dying, quipping to the Doctor that he simply couldn't find the time to die yet (though this may have simply been Constantine recognising he was infected as opposed to signs of a prior illness). Despite this he had persisted with his work in the hospital, even as the Blitz raged around him.
One night in January 1941, Jamie was brought to him as a patient, displaying extreme injuries and was initially declared dead, only for the Child to reanimate, a Gas Mask now affixed to his face and an obsession with finding his 'Mummy'. Dr Constantine tried some experimental therapy with the "empty" child in Room 802 and recorded it — his empathy likely due to losing his child (or children) and grandchild (or grandchildren) to the war. Notably despite Room 802 being secured, Jamie was provided toys, as well as paper and pencils (which he used to obsessively draw 'Mummy') as Constantine attempted to communicate with him.
Over time, every other person in the hospital was infected; first doctors and nurses (starting with those who had attempted to treat Jaime & thus touched him), then patients from the same ward and then gradually every patient in the hospital. Gradually those exposed to Jamie began to transform to become like him, with what appeared to be a gas mask now fused to their flesh.
Despite the pattern of infections around him Constantine continued to care for them and do what he could to keep them comfortable (despite the victims appearing to lack vital signs or needs). He had come to suspect that the Army would bomb the Hospital and blame it on the Germans to contain the plague, but he feared this would be too little, too late; as other isolated cases were already appearing all over London.
By the time the Doctor arrived, Constantine himself was the only one in the hospital, either as a patient, or a member of staff, left unchanged by the plague, though he showed early symptoms such as a scar on his hand. His presence seemed to keep the gas mask zombies subdued, as even after Jaime's escape from Room 802, the other gas mask zombies left in his wake remained passive (responding only to loud noises) while Constantine remained in the hospital.
Constantine invited the Doctor to examine the patients around him, warning him not to touch their flesh & confirming to the incredulous Doctor that every patient in the hospital now showed identical injuries. He provided the Time Lord a rundown of how Jamie had arrived and the pattern of infection left in his wake. Recognising the early signs of his imminent transformation, he urged the Doctor to keep his distance, revealed Room 802's significance and urged him to seek out Nancy's whom he insisted knew more than she would tell Constantine. Before he could say more he finally succumbed to the plague himself and as the Doctor watched a gas mask grew from the physician's face, rendering Constantine a gas mask zombie like the his colleagues and patients.
Just as Constantine's presence had seemed to 'calm' the zombies, his transformation seemed to 'activate' them, as almost immediately after his transformation Jamie became able to (or aware of his ability to) command the gas mask zombies from a distance. Constantine along with the other zombies proceeded to threaten the Doctor, Rose Tyler and Captain Jack Harkness when Jamie found Nancy again. (TV: The Empty Child) The Doctor kept them at bay by sending them to their room, which led Constantine's zombie to return to the chair the physician had been sitting in when he succumbed to the plague.
He was among the victims of the plague summoned to the site of the Chula ship in response to the ship's distress signal. When the nanogenes later recognised the correct human DNA, they repaired all those who had been infected, restoring Constantine, who was able to carry on his good work at the hospital. He was also left rather surprised at the knowledge that one of his patients had regrown her leg due to the nanogenes, to which he could only ask if she miscounted. (TV: The Doctor Dances)
Constantine lost at least one child and at least one grandchild to the Blitz. He stated that he was "a father and a grandfather" before the war began and was now neither but was "still a doctor". The Doctor sympathised with him, saying he "knew the feeling". (TV: The Empty Child)
Dr Constantine was a dedicated doctor to the very end, keeping his patients comfortable despite their conditions and continuing to work around them, despite showing clear awareness that his hospital was Ground Zero of the plague and his continued presence was putting him at greater risk of infection. He regarded his duty as a doctor to be more important than his personal safety, particularly in light of entering World War 2 as both a father and a grandfather and by January 1941, no longer being either, suggesting he had experienced a family tragedy.
He appears to have known Nancy to some degree prior to the incident with Jamie and had attempted to convince her to talk to him about Jamie, knowing her well enough to tell she was keeping things from him, but unable to convince her to open up further.
He was also selfless in death, after recognising the warning signs of his coming transformation; Dr Constantine used his final lucid moments to inform the the Doctor of the need to find & speak with Nancy, the importance of Room 802 and telling him what he could of gas mask zombies' impossible physical conditions before succumbing. (TV: The Empty Child)