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Number of contacts, immunes and susceptibles in successive time periods of transmission

 

Time period

of infectious

transmission

 

(1)

 

Total

number of

contacts

 

(2)

 

Number

immune

 

 

(3)

 

Number

susceptible

and infected

 

(4)

Number

susceptible

and

indirectly

protected

(5)

Fraction of

indirectly

protected

among all

susceptibles

(5)/[(4)+(5)]

t1

1

-

1

-

-

t2

3

1

2

-

-

t3

9

3

4

2

0.33

t4

27

9

8

10

0.56

t5

81

27

16

38

0.70

t6

243

81

32

130

0.80

The table is based on the imaginary example of slides 6-7 (R0=3, 1/3 immune) and gives a feel of the order of magnitude of the effect of indirect protection brought about by herd immunity.

Observe the exponential increase of numbers in columns (2), (3) and (4). Note the progression of the fraction in the last column.

Remember the unrealistic nature of this exercise and the implicit assumptions mentioned in slide 8. A further assumption is that the population is large enough so that the chances of an infected case to meet in the first 6 time periods of transmission presented someone infected in a previous time period (and already immune) are negligible.

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