A herd immunity demonstration.
Try it here: https://op12no2.github.io/indirect/.
As you move the slide the demo executes 1000 SIR models with different initial R representing the x axis.
Herd Immunity Demonstration
The vertical axis represents the percentage of a population infected during an epidemic.
The horizontal axis represents the percentage of the population who were immune at the
start of an epidemic; either through vaccination or previous exposure, recovery and
long lasting immunity.
Thus one vertical slice of the graph represents a whole epidemic.
If the total number of people infected during an epidemic had a linear relationship to the
number of people initially immune, we would expect to see the diagonal line shown.
In reality the total number of people infected is always less than that, as shown by the curved line.
The vertical distance between the two lines represents those people who were indirectly protected.
This is called herd immunity.
This herd effect is greatest at the herd immunity threshold (H) where the percentage of the
population who are infected drops off dramatically; effectively protecting everybody who is
susceptible.
Vaccination schedules target H for this reason and can in some cases
result in total eradication of a disease; smallpox for example.
The virulence of a disease is represented by the basic reproduction number (R0) and
can be thought of as the average number of people somebody will infect during the early
stages of an epidemic.
Use the green slider to change R0.
As R0 increases, H increases () and the shape of the curve changes.
Notice that herd effects other than those at or near H are minimal unless R0 is quite small.
Notice also when nobody is immune at the start of an epidemic (far left of the graph) the
percentage of the population infected is always above 50% and very quickly increases to
near 100% as R0 increases.
Here are some examples of R0:-
COVID-19: 1.5 to 4 (**)
Smallpox: 4 to 7
Rubella: 5 to 7
Mumps 4: to 12
Chickenpox: 10 to 12
Pertussis: 12 to 18
Measles: 12 to 18
Zombies: 20+
() H=1-1/R0
(**) May not give long lasting immunity.