A mathematical model for pertussis transmission and vaccination

Abstract

Pertussis remains an endemic and periodically resurgent vaccine-preventable disease despite long-standing immunisation programmes, reflecting complex interactions between transmission, waning immunity, vaccination history, and heterogeneous clinical presentation. We present a comprehensive age-structured mathematical model of pertussis transmission that explicitly represents infection heterogeneity, immunity dynamics, and detailed vaccination schedules across the life course. The model stratifies the population into 56 age groups and 29 epidemiological states, capturing four distinct infection types that differ by severity, symptoms, and infectiousness, including asymptomatic infection. Both naturally acquired and vaccine-derived immunity are modelled as non-lifelong, incorporating waning, partial protection, reinfection, and immune boosting following exposure without transmissible infection. Vaccination is represented at high resolution, including dose-specific primary series vaccination, booster doses in early childhood, childhood, and adolescence, and maternal immunisation during pregnancy, with differentiation between whole-cell and acellular pertussis vaccine formulations and historical changes in vaccine use and coverage. Periodicity and stochasticity are incorporated to reproduce observed multi-year epidemic cycles. A global sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients identifies immunity waning rates, immune boosting, and recovery from severe infection as key drivers of modelled incidence, mortality, and population protection. By integrating detailed immune processes with realistic vaccination histories, this model provides a flexible framework for evaluating pertussis epidemiology and assessing the population-level impact of alternative vaccination strategies, including booster and maternal immunisation policies.