I think some mathematical intuition is helpful if you want to understand communicable disease transmission.
The basic thing to think about is how many people each infected person in turn infects.
- If the number is less than one, as the infected people get better or die, the number of infected goes down;
- If the number is exactly one, then as each infected person leaves the pool of those communicating the disease, another replaces him/her; the disease becomes endemic;
- If the number is greater than one, the number of infectious people (those communicating the disease to others) grows; the disease becomes epidemic.
There is another, actually common situation, in which the number of new infections per infectious person varies over time. When it is greater than one, the number of infected grows; when it is less than one, the number of infected decreases.
The transmission of the disease depends on the contact rate and the portion of the population that is immune to the disease.
- The contact rate can change; kids are sometimes in school, with a high contact rate with others with "childhood diseases" and sometimes out of school when that contact rate tends to be less.
- The immunity in the population can also change; for example, for many communicable diseases, people who have had the disease and recover are then immune.
When an epidemic starts, public health officials seek to stop it by encouraging people to avoid crowds or by immunizing people with vaccines. In a disease like flu, in which the virus is often communicated by contaminating a hand which then carries the virus to the mouth or nose where it can actually infect the person, hand washing can reduce the actual "contact rate".
We know that the current measles epidemic in the USA was started by a foreign visitor to Disneyland. Measles was essentially eliminated from the United States by massive immunization with a long-lasting immunity from a safe vaccine. However, there are parts of the world where it remains a common disease -- either endemic as new generations of vulnerable kids get the disease, or subject to occasional epidemics. Thus, even after the disease has been eradicated once, if the immunity level is allowed to increase, an infected visitor can start a new epidemic.
In the United States some people are now refusing to allow their children to be immunized against measles. Some do so for religious reasons; some for (unjustified) fear of side effects of the vaccine. While the immunity level in the USA as a whole is high enough that we do not need now to fear a measles pandemic, the vulnerable kids tend to live in the same small communities. One measles is introduced into such a community it may experience a local epidemic of the disease. For an infected child, measles can be a very serious disease!
And of course, a family traveling from a measles free country to one where measles is common, exposes itself to the disease. If that family's children are not immunized, the family is asking for heartbreak!
People who have been infected with HIV tend to live a long time with the infection; indeed, life expectancy of an infected person has increased greatly since effective drugs were developed to help fight the disease.
The curve above shows a rapid increase in the number of infected adults (the prevalence of HIV infection in adults) by continent. That number was increasing rapidly in the 1990s; the rate of increase trailed off in the following decade as public health efforts became more effective.
Canada: Number of New Infections Per Year (estimates)
The Canadian data shows how public health measures dramatically reduced the spread of infections in that country among men who had sex with men (MSM) in the 1980s. The rise in infection among intravenous drug users (IDU) was interrupted in the 1980s. The MSM incidence rebounded in the 2000s; the IDU incidence remained more or less constant during that period.