Reproductive number of pertussis among infants in Wisconsin is 16.00 (Kitala et al, 2002)

Ro = 16.00

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), "; infants (Wisconsis) - Kitala et al (2002)", sep="")
plot (fraction_vaccinated_pertussis, Re, main = "Pertussis" , sub = subtitle, xlab = "Fraction of Population Vaccinated \n", ylab = "Effective Reproductive Number (Re)")

Results and Discussion

Reproductive number of chickenpox among elderly in Egypt is 16.00 (Kitala et al, 2002). 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 heath implications

Recommend pertussis vaccination among infants in Wisconsin at coverage levels of above 93.75%