The peak of the flu arrived after the armistice, but the flu and the war are tied closely together. Without the war, it's unlikely that we'd have had a global pandemic. The best introductory book about the 1918-1919 Spanish Influenza pandemic is John Barry's The Great Influenza: The Story of the Deadliest Pandemic in History. This book answers your question and many more. I suggest it each time this topic comes up.

In any event, the most common and most widely accepted theory about the Spanish Influenza is that it arose in Haskell County Kansas in late 1917 and spread to Camp Funston, a U.S. Army facility, in February 1918. By March, it had spread to other army camps and to nearby U.S. cities, which reported a spike in flu deaths during March and April.

In early April, the disease arrived in Europe, apparently through the port of Brest, which accepted large numbers of American soldiers arriving from North America. It spread across France, hitting Paris in late April and Italy about the same time. British soldiers suffered in May and Britain itself in June.

German soldiers, too, were affected, and the disease hit just as Germany was beginning its last great offensive in the West. No less a figure than Erich von Ludendorff noted the effect it had on his men: "It was a grievous business having to listen every morning to the chiefs of staff's recital of the number of influenza cases, and their complaints about the weakness of their troops.

Ludendorff used influenza as an excuse for the failure of his offensive, but whether or not it was the decisive factor is impossible to say. British, French and American troops were also suffering from the disease, in about the same numbers.

In May, the disease reached Spain in significant numbers, with King Alphonse XIII falling seriously ill. This is when the pandemic got its name, because Spain ─ a neutral party in the war ─ didn't censor information about the disease's spread.

Death rates peaked in England, Scotland and Wales in June and July. Germany had its full-fledged outbreak about the same time. Holland and Sweden, somewhat isolated by the war, were hardest hit in August.

It's important to note, however, that this wave of the disease was only a weak tide compared to what would come later. This wave killed few people, particularly young men, and it sickened them only for two or three days.

As Barry notes on Page 174: "Between June 1 and August 1, 200,825 British soldiers in France, out of two million, were hit hard enough that they could not report for duty even in the midst of desperate combat. Then the disease was gone. On August 10, the British command declared the epidemic over. In Britain itself on August 20, a medical journal stated that the influenza epidemic 'has completely disappeared.'"

But this was only the first wave. Apparently, while in Europe, the disease mutated, adapted or combined with other influenza strains to become much more virulent and deadly. In late August and September, the second wave began, and this one was far more deadly. This wave is the one that gives the pandemic is historical memory.

The first wave seems to have immunized (to some degree) those who caught it. The second wave worked behind the lines, and in the final months of the war, after everything had been largely decided on the battlefield, it performed one final reaping.