The benefits of combining early aspecific vaccination with later specific vaccination

Timing is of crucial importance for successful vaccination. To avoid a large outbreak, vaccines should be administered as quickly as possible. However, during early stages of an outbreak the information on the disease is limited and delaying the intervention enables the design of a more tailored vaccination strategy. In this paper, we study the resulting trade-off between vaccination timing and an effective response strategy. We model disease progression using the seminal SIR model, and consider a decision maker who allocates her budget over two vaccine types: an early aspecific vaccine and a later specific vaccine. We analytically characterize the switching curve separating the parameter space region where the late specific vaccine is preferred from the region where the early aspecific type is preferred. More importantly, we show that the decision maker should not only consider pure strategies, i.e., strategies which spend the entire budget on one of the types. Instead, she should invest in both vaccine types to benefit both from an early response and from an effective vaccine. We prove that at the switching curve, such a hybrid strategy is strictly better than either of the pure strategies due to the non-linear dynamics of epidemics. Our numerical experiments show that a hybrid strategy can reduce the number of infections by more than 50% compared to the best pure strategy. Such experiments also substantiate our restriction to two vaccine types.