The existence of censorship in many countries during WWI (and many other wars) wasn't exactly hidden. Many countries had official structures and organisations for censorship, underpinned by official legislation.
In an article on censorship for the International Encyclopedia of the First World War, Eberhard Dehm writes
While on the continent censorship was introduced in 1914 and justified by the proclamation of the state of siege, in Britain and later in Italy and in the United States the parliamentary bodies had to be consulted. Censorship was thus authorized in Britain by the Defence of the Realm Act (DORA), in Italy by the decree of 23 May 1915, and in the USA by the Espionage and Sedition Acts. Most urgent was the control of the media, and also, somewhat later, of correspondence. All countries rapidly organized central censorship offices: the Oberzensurstelle (Chief Censorship Office) in October 1914 in Berlin, subordinated to the Nachrichtenstelle (Intelligence Bureau) of the Oberste Heeresleitung (Supreme High Command, or OHL), which did not take up its work until February 1915; the Bureau de la Presse (Press Bureau) in Paris under the direction of the Ministry of War; the Official Press Bureau, jokingly called Suppress Bureau, in London; and in April 1917 the Central Censorship Board in the United States.
Even the US military itself has an article on its website on press censorship in World War I. There, they write
The objective of wartime censorship was to prevent the exposure of sensitive military information to the enemy. Similar censorship had been practiced by the U.S. Army in the Civil War and the Spanish-American War. During World War I, however, the press censorship system was formalized and extended, according to the Army's official history, to include anything that might "injure morale in our forces here, or at home, or among our Allies," or "embarrass the United States or her Allies in neutral countries."
Subsection 10F, Press, implemented a form of "voluntary censorship," bolstered by the Espionage Act of June 15, 1917, and the Sedition Act of May 1918, as well as several executive orders. Essentially, in a climate of cooperation fueled by patriotism and common sense, journalists dutifully avoided writing about topics recommended off-limits by the military.
We can savely assume that widespread knowledge about outbreaks of a severe disease would have been considered to "injure morale". Therefore, either the press would avoid the topic on its own, or the censorship structures as outlined by the quotes above would remove any articles on the topic.