Complementarity between term-time forcing and delayed vaccination response in explaining irregular dynamics in childhood diseases

This paper investigates an SIR model with the following properties: (i) demographics are present. (ii) The fraction vaccinating at any time is dependent on past levels of disease prevalence with distributed delay. (iii) The maximum fraction vaccinating is bounded below one by medical contraindications or unshakeable beliefs among a sub-set of the population that the vaccination is not beneficial. (iv) Disease transmissibility is higher when school is in session than when it is not. Our main findings are that the time series of prevalence can exhibit irregular inter-epidemic intervals, and the profile of outbreaks can be highly variable over time-sometimes exhibiting single large peaks and sometimes clusters of closely-spaced lesser peaks.