Le superflu, chose tres necessaire -- Voltaire
Although the history of flu epidemics is non-mathematical, in this case, as Voltaire might say, the superfluous is very necessary.  In 1918, when the world population was 1.8 billion, an influenza epidemic incapacitated 1 billion and killed 20 million, all within the space of 8 weeks.  Most of the people who died were in their thirties.  For comparison, 8.5 million people died in World War I (Jun 1914 - Nov 1918), and 55 million died in World War II (Sep 1939 - Sep 1945).  In fact, the turning point of WWI happened while the German Chancellor was bedridden with influenza.  Desiring to wake up fresh, he accidentally overdosed on a sleeping tonic.  During his subsequent coma, the german defenses collapsed. [Encyclopedia Britannica, 1949]

Can it happen again?  In April 1983, a variety of the influenza virus killed 20 million chickens in Pennsylvania.  The virus proved lethal because of a change in one animo acid. [The Transmission of Epidemic Influenza, Hope-Simpson 1992]  Mild flu epidemics happen every year.  Whenever a large population of non-immunes exists, epidemics can happen.  In 1875, The King of the Fiji Islands returned from a diplomatic trip, infected with measles.  Out of a population of 150 thousand, 40 thousand died of measles. [Influenza, An Epidemilogic Study, Vaughn 1921]

The spread of flu has a strong mathematical basis.  Serfling's model ( (Y=average mortality + trend + 52 week cycle + 26 week cycle + Error) or (Y = a + b1t + b2cos(p t / 26) + b3sin(p t / 26) + b4cos(p t / 26) + b5cos(p t / 26) + E ) ), for instance, is used to estimate levels of influenza.  The Kermack-McKindrick model (Susceptibles --rIS--> Infectives --qI--> Quarantines) can be used to model the spread of an epidemic.  For fun, I used it to model the 1918 virus in today's world.  I collected some data first.

Worldwide influenza epidemics have occurred in the following years: 1732, 1781, 1802, 1830, 1847, 1857, 1918, 1957, and 1968. [Influenza, The Last Great Plague, Beveridge 1977].  Coincidentally, both the 1957 'Asian' flu and the 1968 'Hong Kong' flu both started during a month of record breaking sunspot activity. [The Diffusion of Influenza, Pyle 1986].  Here are a few words on the 1918 flu:

The total mortality of the 1918 epidemic was 0.5 percent of the population.  In a few places the mortality was much higher.  In Samoa 25 percent of the people died.  The Eskimoes in Alaska suffered terribly; some villages were wiped out and others lost their entire adult population.  In Nome, 176 out of 300 Eskimoes died.  The disease caused havoc in India where and estimated five million people died. [Beveridge]
When a population is suddenly stricken, uninfected people must work much harder to maintain the normal quality of available services.  In particular, medical services can be overwhelmed, prompting an increase in the mortality rate.  Remember, when half the population is sick, that means half the hospital staff is sick.  Out of all the major United States cities, only Boston adequately confronted the 1918 flu.  With a few days notice, the hospitals of Boston worked with city residents to form an enormous volunteer force.  It worked -- the mortality rate in Boston was much lower than in other cities.  [Vaughn, 1921]  I wonder if today's hospitals know this?

One unique feature of the 1918 'Spanish' flu was that it traveled in waves.  Here's what ABC News said about it.  The first and last waves were more or less normal epidemics.  It was the second wave, likely a mutation of the first, that offered a significant mortality figure.  World War I intensified these waves.  Massive troop movements, the development of fronts, and so on -- these factors led to a homogenous mixing of the human population unlike anything seen previously.  In the present day, this sort of mixing happens routinely and constantly.

Does influenza threaten the existence of mankind?  Probably not.  Mutations of the flu virus sometimes have high mortality rates among avian species, but the 1918 flu is the worst that mankind has had to face.  However, influenza will definitely annoy mankind.  (It wiped me out this weekend.)  Mathematical modeling can be used to find ways to lessen this impact.

[Here is the C code of my model

The following results apply to the United States population only.
Q: Are Airports a major factor in the spread of flu?
A: Yes.  In this model, they increase the speed at which the flu spreads.  But mortality figures were unaffected.  Shutting down airports and restricting road travel will slow an epidemic, but will not dull its bite.  When other factors are included (notably: immunizations), airport shutdowns save lives.  Perhaps "Do you have any flu-like symptoms?" could be added to the current list of boarding questions.
Q: How helpful are Hospital volunteers (as Boston 1918) ?
A: Very!  Without volunteers, 3.01 million people die in the model.  With volunteers, 1.91 million people die. In my model, I assumed that the death rate might go as high as 4% if an area is overwhelmed.  This is not an unreasonable assumption.  During the worst phase of the epidemic, many millions of people will need health care daily.  In the model, a massive hospital volunteer program saved 140 thousand lives in one day.
Q: How can early immunizations affect an epidemic?  Late immunizations?
A: The earlier the immunizations begin, the better.  If 2% of the population can be immunized daily, starting 2 weeks after the initial outbreak, the model shows that the lives of 1 million will be saved.
Q: Can the news media help/hinder in the event of an epidemic?
A:  I couldn't figure out how to model this.  They can help by spreading information.  In a massive epidemic, a primary killer is not knowing how to care for the sick [Vaughn, 1921].  The media can serve as an adjunct to the hospital volunteer workforce, described above.  On the other hand, the media could easily add even more panic to an already horrifying epidemic.

Model results: With rapid immunizations, block by block hospital volunteers, and increased airport vigilance, 1.23 million die in twelve weeks.  Without those things, 3.01 million die in ten weeks.  Considering the sheer number of lives that might be saved, plans for implementing a hospital volunteer workforce program should be prepared, if they do not already exist.