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 = 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), "; Rubella", 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, rubella will be eliminated at these higher levels of vaccination coverage.

Public Health Implications

Recommend rubella vaccination coverage levels of above 85.71%.