1. RABIES

Reproductive number of rabbies among dogs in Kenya is 2.44 (Kitala et al, 2002)

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). The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 59.02%; that is, at this level of vaccination coverage, 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 these higher levels of vaccination coverage.

Public health implications

Recommend rabies vaccination among dogs in Kenya at coverage levels 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_measles = seq (0, 1, 0.1)

print fraction of population vaccinated.

cat ("Fraction of population vaccinated:", fraction_vaccinated_measles)
## 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_measles)

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

Reproductive number of measles is 14. The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 92.86%; that is, at this level of vaccination coverage, effective reproductive number is 1 (Re = 1). When vaccination coverage is above 92.86%, effective reproductive number is less than 1 (Re < 1); thereby, measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend measles vaccination among the population at coverage levels of above 92.86%.

  1. PERTUSSIS

Reproductive number of pertussis is 16

Ro = 16

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

fraction_vaccinated_pertussis = seq (0, 1, 0.1)

print fraction of population vaccinated.

cat ("Fraction of population vaccinated:", fraction_vaccinated_pertussis)
## 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_pertussis)

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 = "pertussis" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

Reproductive number of pertussis is 16. The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 93.75%; that is, at this level of vaccination coverage, effective reproductive number is 1 (Re = 1). When vaccination coverage is above 93.75%, effective reproductive number is less than 1 (Re < 1); thereby, measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend pertussis vaccination among the population at coverage levels of above 93.75%.

  1. CHICKEN POX

Reproductive number of Chicken pox is 10

Ro = 10

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

fraction_vaccinated_chickenpox = seq (0, 1, 0.1)

print fraction of population vaccinated.

cat ("Fraction of population vaccinated:", fraction_vaccinated_chickenpox)
## 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_chickenpox)

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 = "chickenpox" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

Reproductive number of chicken pox is 10. The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 90%; that is, at this level of vaccination coverage, effective reproductive number is 1 (Re = 1). When vaccination coverage is above 90%, effective reproductive number is less than 1 (Re < 1); thereby, measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend chicken pox vaccination among the population at coverage levels of above 90%.

  1. MUMPS

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_mumps = seq (0, 1, 0.1)

print fraction of population vaccinated.

cat ("Fraction of population vaccinated:", fraction_vaccinated_mumps)
## 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_mumps)

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

Reproductive number of mumps is 12. The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 91.67%; that is, at this level of vaccination coverage, effective reproductive number is 1 (Re = 1). When vaccination coverage is above 91.67%, effective reproductive number is less than 1 (Re < 1); thereby, measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend mumps vaccination among the population at coverage levels of above 91.67%.

  1. RUBELLA

Reproductive number of Rubella is 7

Ro = 7

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

fraction_vaccinated_rubella = seq (0, 1, 0.1)

print fraction of population vaccinated.

cat ("Fraction of population vaccinated:", fraction_vaccinated_rubella)
## 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_rubella)

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

Reproductive number of rubella is 7. The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 85.71%; that is, at this level of vaccination coverage, effective reproductive number is 1 (Re = 1). When vaccination coverage is above 85.71%, effective reproductive number is less than 1 (Re < 1); thereby, measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend rubella vaccination among the population at coverage levels of above 85.71%.

  1. POLIO

Reproductive number of Polio is 6

Ro = 6

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

fraction_vaccinated_polio = seq (0, 1, 0.1)

print fraction of population vaccinated.

cat ("Fraction of population vaccinated:", fraction_vaccinated_polio)
## 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_polio)

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

Reproductive number of polio is 6. The graph illustrates that as fraction of population vaccinated increases, effective reproductive number decreases. Herd immunity threshold is 83.33%; that is, at this level of vaccination coverage, effective reproductive number is 1 (Re = 1). When vaccination coverage is above 83.33%, effective reproductive number is less than 1 (Re < 1); thereby, measles will be eliminated at these higher levels of vaccination coverage.

Public health implications

Recommend polio vaccination among the population at coverage levels of above 83.33%.