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 are administered preferably as quickly as possible. However, in the early stages of an outbreak the information on the disease is limited and waiting with the intervention allows to design a more tailored vaccination strategy. In this paper we study the resulting tradeoff between timing of vaccination and the effectiveness of the response. 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 suitably invest in both vaccine types to benefit both from the early response and from the good 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. Numerical experiments show that the associated benefit of hybrid strategies over pure strategies in terms of reduction of the number of infections may be more than 50%. Such experiments also substantiate our restriction to two vaccine types.