1. RABIES

Reproductive number of rabies among dogs in Kenya is 2.44 ( Kitata et al)

Ro=2.44

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 2.44 2.196 1.952 1.708 1.464 1.22 0.976 0.732 0.488 0.244 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.5901639

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; dogs (Kenya) - Kitala et al (2002)", sep="")
plot (fraction_vaccinated, Re, main = "Rabies" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion Reproductive number of rabies among dogs in Kenya is 2.44 (Kitala et al, 2002).Herd immunity threshold is 59.02%; that is at this level of vaccination covergae, effective reproductive number is 1 (Re=1). When vaccination coverage is above 59.02%, effective reproductive number is less than 1 (Re<1); thereby rabies will be eliminated at the higher level of vaccination coverage.

Public health implications Rabies vaccine is recommended in Kenya among the dogs at a coverage level of above 59.02%.

  1. MEASLES Reproductive number of Measles is 14.
Ro=14

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 14 12.6 11.2 9.8 8.4 7 5.6 4.2 2.8 1.4 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.9285714

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; people", sep="")
plot (fraction_vaccinated, Re, main = "Measles" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

The reproductive number of Measles is 14. The graph shows that as the fraction of the population vaccinated increses, effective reproductive number decreases. The herd immunity threshold is 92.86% , at this level of vaccination coverage in people, the effective reproductive number is 1. When vaccination coverage is above 92.86%, effective reproductive number is less than 1.So the measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend measles vaccines among people at the coverage level of above 92.86%.

  1. PERTUSIS

The reproductive number of pertusis among people is 16.

Ro=16

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 16 14.4 12.8 11.2 9.6 8 6.4 4.8 3.2 1.6 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.9375

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; people", sep="")
plot (fraction_vaccinated, Re, main = "Pertusis" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion The reproductive number of pertusis is 16. The graph shows that as the fraction of the population vaccinated increses, effective reproductive number decreases. The herd immunity threshold is 93.75% , at this level of vaccination coverage in people, the effective reproductive number is 1. When vaccination coverage is above 93.75%, effective reproductive number is less than 1.So the pertusis will be eliminated at these higher levels of vaccination coverage.

Public health implications Recommend pertusis vaccines among people at the coverage level of above 93.75%.

  1. CHICKEN POX

The reproductive number of chicken pox among people is 10.

Ro=10

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 10 9 8 7 6 5 4 3 2 1 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.9

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; people", sep="")
plot (fraction_vaccinated, Re, main = "chicken pox" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

The reproductive number of chicken pox is 10. The graph shows that as the fraction of the population vaccinated increses, effective reproductive number decreases. The herd immunity threshold is 90% , at this level of vaccination coverage in people, the effective reproductive number is 1. When vaccination coverage is above 90% effective reproductive number is less than 1.So the chicken pox will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend chicken pox vaccines among people at the coverage level of above 90%.

5 MUMPS The reproductive number of mumps is 12.

Ro=12

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 12 10.8 9.6 8.4 7.2 6 4.8 3.6 2.4 1.2 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.9166667

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; people", sep="")
plot (fraction_vaccinated, Re, main = "mumps" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

The reproductive number of Mumps is 12. The graph shows that as the fraction of the population vaccinated increses, effective reproductive number decreases. The herd immunity threshold is 91.67% , at this level of vaccination coverage in people, the effective reproductive number is 1. When vaccination coverage is above 91.67%, effective reproductive number is less than 1.So the mumps will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend mumps vaccines among people at the coverage level of above 91.67%.

6 RUBELLA

The reproductive numbe rof rubella among people is 7.

Ro=7

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 7 6.3 5.6 4.9 4.2 3.5 2.8 2.1 1.4 0.7 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.8571429

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; people", sep="")
plot (fraction_vaccinated, Re, main = "rubella" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

The reproductive number of rubella is 7. The graph shows that as the fraction of the population vaccinated increses, effective reproductive number decreases. The herd immunity threshold is 85.71% , at this level of vaccination coverage in people, the effective reproductive number is 1. When vaccination coverage is above 85.71%, effective reproductive number is less than 1.So the rubella will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend rubella vaccines among people at the coverage level of above 85.71%.

7 POLIO The reproductive number of polio among people is 6.

Ro=6

Generate sequence of numbers for fraction of population vaccinated from 0 to 1 with 0.1 interval

fraction_vaccinated= seq(0,1,0.1)

Print fraction of population vaccinated.

cat("Fraction of population vaccinated:", fraction_vaccinated)
## Fraction of population vaccinated: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Compute effective reproductive number.

Re=Ro*(1-fraction_vaccinated)

Print effective reproductive number

cat("Effective reproductive number:", Re)
## Effective reproductive number: 6 5.4 4.8 4.2 3.6 3 2.4 1.8 1.2 0.6 0

Compute herd immunity threshold

herd_immunity_threshold=1-(1/Ro)

Print herd immunity threshold

cat("herd immunity threshold= ", herd_immunity_threshold)
## herd immunity threshold=  0.8333333

Plot fraction of population vaccinated (versus) effective reproductive number.

subtitle = paste ("Ro = ", Ro, ", herd immunity threshold = ", round (herd_immunity_threshold, digits = 4), "; people", sep="")
plot (fraction_vaccinated, Re, main = "polio" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

The reproductive number of polio is 6.The graph shows that as the fraction of the population vaccinated increses, effective reproductive number decreases. The herd immunity threshold is 83.33%, at this level of vaccination coverage in people, the effective reproductive number is 1. When vaccination coverage is above 83.33%, effective reproductive number is less than 1. So the polio will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend polio vaccines among people at the coverage level of above 83.33%.