The seasonally fluctuating densities of M. natalensis were modelled using a seasonal birth-pulse function, B(t)=k exp[−s cos2(πt−φ)], as described in Peel et al. . This is a flexible function in which a synchrony parameter (s) determines the length of the birth period, and another parameter (φ) determines the timing of the birth period. Parameter k ensures that the annual population size remains the same, by compensating the number of births for the (constant) mortality rate μ . Note that this means that while the annual population size is constant, population densities do fluctuate seasonally because all births happen within a few months, whereas deaths happen throughout the year. Function parameters were fitted visually to a 20-year dataset of monthly population densities of M. natalensis in Tanzania ( and more recent unpublished data (H Leirs, up to 2017); electronic supplementary material, figure S1–1). This deterministic demography was used as a basis for modelling demography in the stochastic SIR model (described below) in order to avoid the influence of stochastic changes in population density, and because this reduces the number of simulations that need to be performed.