Dynamical crises, multistability and the influence of the duration of immunity in a seasonally-forced model of disease transmission

Abstract

BACKGROUND: Highly successful strategies to make populations more resilient to infectious diseases, such as childhood vaccinations programs, may nonetheless lead to unpredictable outcomes due to the interplay between seasonal variations in transmission and a population's immune status.METHODS: Motivated by the study of diseases such as pertussis we introduce a seasonally-forced susceptible-infectious-recovered model of disease transmission with waning and boosting of immunity. We study the system's dynamical properties using a combination of numerical simulations and bifurcation techniques, paying particular attention to the properties of the initial condition space.RESULTS: We find that hig..