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), "; Mumps", 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 91.67%. 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, mumps will be eliminated at these higher levels of vaccination coverage.

Public Heath Implications

Recommend mumps vaccination coverage levels of above 91.67%.