The Interaction between Seasonality and Pulsed Interventions against Malaria in Their Effects on the Reproduction Number

<div><p>The basic reproduction number (<i>R</i>₀) is an important quantity summarising the dynamics of an infectious disease, as it quantifies how much effort is needed to control transmission. The relative change in <i>R</i>₀ due to an intervention is referred to as the effect size. However malaria and other diseases are often highly seasonal and some interventions have time-varying effects, meaning that simple reproduction number formulae cannot be used. Methods have recently been developed for calculating <i>R</i>₀ for diseases with seasonally varying transmission. I extend those methods to calculate the effect size of repeated rounds of mass drug administration, indoor residual spraying and other interventions against <i>Plasmodium falciparum</i> malaria in seasonal settings in Africa. I show that if an intervention reduces transmission from one host to another by a constant factor, then its effect size is the same in a seasonal as in a non-seasonal setting. The optimal time of year for drug administration is in the low season, whereas the best time for indoor residual spraying or a vaccine which reduces infection rates is just before the high season. In general, the impact of time-varying interventions increases with increasing seasonality, if carried out at the optimal time of year. The effect of combinations of interventions that act at different stages of the transmission cycle is roughly the product of the separate effects. However for individual time-varying interventions, it is necessary to use methods such as those developed here rather than inserting the average efficacy into a simple formula.</p>