Mr Bleibner, the American sponsor of the Egyptian expedition, is named Felix in the TV episode.
Dr Tosswill, the head of the British contingent of the expedition from the story is now Dr Fosswell.
Curse of the Pharaoh: Exploited by the murderer, who used the fact that he and the murder victims were all members of an expedition that unearthed a Pharaoh's tomb.
Doing In the Wizard: Part of Poirot's role is to show that the deaths at the expedition were not caused by a supernatural element.
Driven to Suicide: Rupert Bleibner shoots himself after learning he had contracted leprosy. The leprosy was a fabrication, however.
Dwindling Party: Four members of the expedition that unearthed the tomb of the fictional Pharaoh Men-her-Ra die one after the other in tragic circumstances.
Exact Words: Rupert Bleibner's suicide note makes mention of him being a leper that everyone assumes is metaphorical, until Poirot points out at the summation that he meant it literally.
The Farmer and the Viper: How does Dr Ames repay Rupert Bleibner making him his heir back at Yale? By murdering his uncle and gaslighting him into committing suicide.
Inheritance Murder: Dr Ames kills Felix Bleibner and convinces his friend Rupert Bleibner to kill himself all in a bid to acquire the Bleibner family fortune, which he'd been made the heir of due to Rupert's gratitude for saving his life.
Morally Ambiguous Doctorate: Dr Ames exploits his medical knowledge to kill three people, directly or indirectly. He lets a wound get infected to make one victim develop septicemia, he gaslights another victim into thinking he has leprosy, killing himself in the process, and he injects another with tetanus while making people think he was administering the antitoxin.
Never One Murder: Zigzagged. Of the four people who die, only two were dead by the killer's own hands; Sir John Willard died of a natural heart attack while Rupert Bleibner killed himself (though only after the killer gaslit him into doing so). While Henry Schneider had nothing to do with the scheme, he was killed in order to help maintain the illusion that it was the Pharaoh's curse at work.
Paranoia Gambit: Dr Ames exploits Rupert's hypochondria by insinuating that the eczema he had on his hand was the early stages of leprosy, and even showed him a vial of chaulmoogra oil (used to treat leprosy before modern drugs) to reinforce that notion. It's enough to make poor Rupert kill himself.
The deaths at the expedition seem to indicate that Sir Guy Willard, the son of Sir John Willard, would be the real target due to his father being the first to die and people dropping like flies soon afterwards. In reality, he was in no danger at all, especially after the true killer was revealed.
Dr Fosswell is shown to be a possible suspect, given that his Patriotic Fervor showed his disdain towards the American side of the expedition, and three of the four deaths were American. He's shown to be not involved with the murders whatsoever.
Spared by the Adaptation: Oddly enough, the killer doesn't die by dosing himself with cyanide, and instead is cornered by Poirot at The Summation and is prevented from using a gun by Hassan, the Willards' Egyptian servant.
