Mathematical epidemiologists create far more complex models than the simulations above to answer three key questions about outbreaks: How contagious is it? How quickly will it spread? And how many people will it kill? These models help public health officials develop strategies to attack specific outbreaks. Read related article.

Compared to other infectious diseases, Ebola spreads slowly and to relatively few people. But it is extremely deadly : The World Health Organization said 70 percent of cases in this year's outbreak are fatal.

Ebola, SARS and chicken pox take roughly the same amount of time to pass from one sick person to the next group of people, called a "generation." If Ebola were as easy to catch as chicken pox, thousands of people would have been sickened by the fourth generation.

By the numbers

Disease Avg. Reproductive ratio Avg. Serial interval Avg. fatality rate Ebola 1.5-2 9-15 70% Smallpox 5-7 14-16 30% Measles 12-18 10-14 0.3-28% SARS 2-3 8-9 11% Diphtheria 6-7 26 5-20% Whooping cough 12-17 19-28 0.1-1% Flu 2-6 3-5 .4-4% Rubella 5-7 15-23 0.05% Mumps 4-7 18-19 0.0001% Chicken pox 3-17 14-16 0.00001-0.0001%

Why do these squares look different every time? Disease estimations rarely have precise, neat numbers. One outbreak may spread more quickly or kill a higher percentage of people than another. So our models run different scenarios based on ranges provided to us by mathematical epidemiologist Gerardo Chowell of Arizona State University. Each sample of 100 starts with a “Patient 0,” the first person to get sick. After that, each simulation may differ in the number of days before the next group of people becomes ill, the number of people in that group, and the percentage of them who die.

The average reproductive ratio is a measure of how easily a disease travels from person to person. A rate of 5 means each sick person passes the disease to an average of five other people. When the number is below 1, the epidemic dies out.

The average serial interval is the length of time between the first patient showing symptoms and a secondary case showing symptoms. The longer the better, because that allows time to find and isolate people who have been exposed before they spread the virus.

Knowing the fatality rate helps set priorities, from allocating money to fight the disease to deciding whom to immunize. If a disease kills more children or elderly people, for instance, they may get priority if vaccine supplies are limited. When an Ebola vaccine is ready, healthcare workers probably will receive the first doses.