IOTL, Theodore Roosevelt, the POTUS from 1901 - 1909 and the Progressive Party nominee for President in 1912, died in 1919 at the age of 60. It was rumored that he was planning to run for President once again in 1920.
TR's cause of death was a preventable one - malaria, which he had contracted on one of his safaris years previously. It's pretty easy to butterfly his malaria away - he lived through a dozen safaris throughout his lifetime, he could live through another, especially as he's TR.
Now, here's the rub: Along with not catching malaria in 1918, TR
never contracts malaria. Instead, he continues his record of good health and, in a shocking anomaly, Theodore Roosevelt dies on his 100th Birthday - October 27, 1958.
What effect would TR have on the world if he lived from 1919 - 1958? Would he have been elected President in 1920? Would he have been re-elected to a fourth term in 1924? What would he have done after his presidency? Would he run for President a fifth time? What's your opinion on the last forty years of TR's alternate life?