Fighting Transient Epidemics - Optimal Vaccination Schedules Before and After an Outbreak

Throughout history, epidemics have been a recurring terror to humanity. In vulnerable societies prior to the development of modern medicine an epidemic could wipe out 50-60% of a population. With the possible exception of AIDS, modern epidemics are less devastating to affected communities, but still impose large costs on society. Even more mundane diseases such as influenza impose large costs. A bad outbreak of the flu that causes, say, 10% of the population to loose on average 5 working days, represents a severe economic cost to society no matter how trivial the disease is. On the other hand, viruses such as the Ebola virus with a fatality rate close to 90% cause considerable harm to small contained areas even if the extreme mortality in itself prevents the disease from spreading to affect large populations. Recent diseases such as SARS and the possibility of a bird flu epidemic have underscored the importance of transient epidemics to human welfare. One common feature of many epidemics is that they tend to move through a population and then disappear. The epidemic may reappear later, possibly in a mutated form, but still represents disjoint events. To my knowledge this class of epidemic has not yet been analysed in the economic literature. Often outbreaks these epidemics are predicted, leading to the additional question of how to implement preparatory health policies anticipating the outbreak. The present paper thus fills two important gaps in the literature. First we analyse optimal vaccination policy for an epidemic that eradicates itself. Second, we analyse optimal preparatory vaccination schedules. Optimal preventive policies are likely to depend on parametersthat are intrinsically uncertain. Here we first analyse the deterministic case and use this analysis as a stepping stone for the case where there is uncertainty about if and when the epidemic starts as well as about the parameters in the model.