Interestingly enough, the US military is among the most highly vaccinated group of people in the country. For us, vaccinations are mandated - everything from flu and plague to H1N1 and Smallpox. Some of us (I am one of them) even choose to get the Anthrax vaccinations. And without a doubt we are among the healthiest segment of the population in the entire country. I have not had the flu now for over a decade. I have never had any kind of serious contagious disease since I first put on the uniform in 1983.
And even though we live in close quarters, often times 40-50 living in a single room with shared bath and toilet facilities, the spreading of any disease other then the common cold is very rare. This is because of all the inoculations we get both when we join, as well as updates and new ones every few months.
In fact, I remember in the 1980's when typically every 2-3 years most bases and units had at least one outbreak of Hepatitis. On 2 different occasions in 10 years I was quarantined on base, unable to leave for 2-7 days because of such an outbreak. Not able to leave the barracks, once even having to sleep on the floor for 3 days because I was married and could not go home. But in the 8 years since I rejoined no base I have been on has ever had an outbreak of Hepatitis. This is simply because it is one of the mandatory vaccines we get every year.
And as for vaccines not allowing a disease to spread, that is very true. It is known as "Herd Immunity". The more people who are inoculated, the harder it is for a virus or bacteria to spread through the population. The less people are inoculated, the easier it is for a contagion to spread to others.
This is really a very simple math exercise. If you want to see how fast a contagion can spread without a vaccine, study a virus that has none available. H1N1 early on, SARS, HIV, or even Ebola in Africa. With no vaccination the virus spreads like wildfire. I myself, I have not forgotten how devastating HIV was to segments of our population in the 1980's. Every homosexual male I knew in High School is now dead because of this. And yes, I knew 5. All graduated from Van Nuys High School from 1982-1985. All 5 were dead by 1990 from AIDS. This is what a virus can do in a population that is not vaccinated.