AN AGE-STRUCTURED MODEL FOR PERTUSSIS TRANSMISSION WITH MULTIPLE INFECTIONS STUDYING THE EFFECTS OF CHILDHOOD DTAP AND ADOLESCENT TDAP VACCINES

Abstract

An age-structured deterministic model with multiple infections that accounts for decaying maternal antibody, waning infection-acquired and vaccine-induced immunity is formulated to study the transmission dynamics of pertussis and the effect of childhood DTaP and adolescent Tdap vaccines. The expression of the reproduction number [Formula: see text] is derived for the ODE model in the case of proportionate mixing. Estimated age-dependent transmission probability and empirical contact data are used in the simulation of the ODE model from which the basic reproduction number [Formula: see text] is estimated to be around 15. The combination of DTaP and Tdap vaccines fails to bring [Formula: see text] under one and thus pertussis remains endemic despite sustained high coverage of vaccination. While both DTaP and Tdap vaccines have remarkable effect on reducing the incidences of the age groups being directly vaccinated, the adolescent booster dose Tdap is also found to provide some indirect protection for infants though very limited ([Formula: see text] incidence reduction).