How do R and vaccination decide whether an Ebola epidemic ends?
An epidemic ends when each case infects fewer than one other person, and for Ebola that takes far fewer immune people than for measles.
An epidemic ends when each case infects fewer than one other person, and two things push that number down: stopping contacts between the sick and the healthy, and making people immune. R0 is the average number of people infected by a single infectious individual in a population with no prior immunity. When the is reduced to and sustained below 1 new individual per infection, the number of cases gradually decreases until the disease has been eliminated.
Immune people act as a barrier in the spread of disease, slowing or preventing its transmission to others, whether the immunity comes from infection or from vaccination. When a critical proportion of the population becomes immune, called the herd immunity threshold, the disease may no longer persist in the population. The threshold depends on R0: it is 1 โ 1/R0, so an R0 of 2 needs half the population immune, and an R0 of 4 needs three quarters.
Ebola's numbers are on the low side. In September 2014 the estimated R0 was 1.71 for Guinea, 1.83 for Liberia and 2.02 for Sierra Leone, which by that formula puts the threshold at about 42, 45 and 50 percent. Measles, by contrast, is an example of a disease with a high threshold, exceeding 95 percent. That is part of why Ebola can be stopped without immunising everyone: vaccinates those most likely to be infected, and, along with isolation and safe burials, it pulls R down where the virus actually is.
Share who must be immune, by a simple calculation (1 โ 1/R0)
| Immune needed | |
|---|---|
| Guinea 2014 (R0 1.71) | 42% |
| Liberia 2014 (R0 1.83) | 45% |
| Sierra Leone 2014 (R0 2.02) | 50% |
| Measles (more than) | 95% |
West African data suggested that response strategies that achieved 60 percent efficacy for , case isolation and contact tracing combined could have ended that outbreak after only 6 months. Vaccines have a limit too: if a vaccine's is less than 1 โ 1/R0, eliminating a disease is impossible even if the entire population is vaccinated.
Try it
How much immunity stops it?
It keeps growing
- Each case now infects
- 2
- Cases after 6 rounds
- 127
- Vaccinated to stop it
- 50%
Challenge ยท Start with R at 2, near the 2014 estimates, and raise the vaccinated share until each case infects fewer than one. Then try R at 4 and see how much more is needed.
Quiz me
0/3
Recap
The epidemic ends when R falls below 1: cutting contacts and adding immunity both push it down.
๐ก A trick to remember it ยท One over R is the share that may stay unprotected; the rest is the wall that must be built.
Surprising fact ยท With an R0 of about 2, the threshold for Ebola is about 50 percent, against more than 95 percent for measles.
Sources (6)
No source, no claim. Every fact in this lesson (11 claims) cites at least one of these.