Vaccinating in disease-free regions: a vaccine model with application to yellow fever

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Abstract
Concerns regarding natural or induced emergence of infectious diseases have raised a debate on the pros and cons of pre-emptive vaccination of populations under uncertain risk. In the absence of immediate risk, ethical issues arise because even smaller risks associated with the vaccine are greater than the immediate disease risk (which is zero). The model proposed here seeks to formalize the vaccination decision process looking from the perspective of the susceptible individual, and results are shown in the context of the emergence of urban yellow fever in Brazil. The model decomposes the individual's choice about vaccinating or not into uncertain components. The choice is modelled as a function of (i) the risk of a vaccine adverse event, (ii) the risk of an outbreak and (iii) the probability of receiving the vaccine or escaping serious disease given an outbreak. Additionally, we explore how this decision varies as a function of mass vaccination strategies of varying efficiency. If disease is considered possible but unlikely (risk of outbreak less than 0.1), delay vaccination is a good strategy if a reasonably efficient campaign is expected. The advantage of waiting increases as the rate of transmission is reduced (low R 0 ) suggesting that vector control programmes and emergency vaccination preparedness work together to favour this strategy. The opposing strategy, vaccinating pre-emptively, is favoured if the probability of yellow fever urbanization is high or if expected R 0 is high and emergency action is expected to be slow. In summary, our model highlights the nonlinear dependence of an individual's best strategy on the preparedness of a response to a yellow fever outbreak or other emergent infectious disease.