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), "; Measles", 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 coverage levels of above 92.86%.