
An epidemic starts with one deceased person that infects others, etcetera...
The decease spreads among the population.
Recovered persons are immune so from a certain moment the decease will disappear
because too many people have obtained immunity.
The virus dies because of the lack of hosts.
However: at which moment will this situation occur?
Here is a simple formula.
1.
Say one person infects N others.
2.
Say I is the part of the population that is immune.
(1  I) is the part that has not yet gained immunity.
3.
(1  I)N is the real number of people that are infected by one person.
4.
The decease will no longer spread if :
(1  I)N < 1
N  IN < 1
IN > N  1
I > (N  1)/N
I > 1  1/N
Examples:
If one person infects 3 others than is needed: I > 1  1/3 = 67%
If 67% of the population is immune, the decease will stop.
Measles is a very contagious desease.
If a child infects 20 others, the percentage of children that requires vaccination is
1  1/20 = 95% to avoid spreading.

