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

Public Health Implications

Recommend pertussis vaccination coverage levels of above 93.75%.