Four small formulas carry most of epidemiology. Incidence counts new cases. Prevalence counts all cases at once. R0 says how hard a microbe pushes. And the herd immunity threshold says how much of a population you have to cover to stop it. Move the sliders and every number is worked out in front of you.
The populationeach dot stands for a slice of it
immuneexisting casesnew cases this yearstill at risk
Incidence
0
new cases per 100,000 per year
Prevalence
0
all cases per 100,000, right now
Generation by generationeach round of spread
Set the slidersthe model reads them live
The numbers you feed itdrag any one
1,000,000
80,000
7 d
1.3
0%
At risk
0
Existing cases
0
R now
0.0
Load a real disease
Herd immunity threshold1 − 1 ÷ R0
R0 for real diseases, and what each one needs
Notice the shape of it. Push R0 up and the threshold climbs fast at first, then flattens near 100 percent. That is why measles demands such high coverage, and why a small dip in uptake brings it straight back.