Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: a theoretical study This is a draft. The final version has been published on Mathematical Bio- sciences and Engineering, Volume 9, Number 3, pp. 539–552, July 2012 Bruno Buonomo and Eleonora Messina Department of Mathematics and Applications, University of Naples Federico II via Cintia, I-80126 Naples, Italy. buonomo@unina.it, eleonora.messina@unina.it Abstract When a newly emerging human infectious disease spreads through a host population, it may be that public health authorities must begin facing the outbreaks and planning an intervention campaign when not all inter- vention tools are readily available. In such cases, the problem of finding optimal intervention strategies to minimize both the disease burden and the intervention costs may be addressed by considering multiple interven- tion regimes. In this paper, we consider the scenario in which authorities may rely initially only on non-pharmaceutical interventions at the begin- ning of the campaign, knowing that a vaccine will later be available, at an exogenous and known switching time. We use a two–stage optimal con- trol problem over a finite time horizon to analyze the optimal intervention strategies during the whole campaign, and to assess the effects of the new intervention tool on the preceding stage of the campaign. We obtain the optimality systems of two connected optimal control problems, and show the solution profiles through numerical simulations. Subject class: 92D30, 49J15 Keywords: two–stage, optimal control, epidemic models, non-pharmaceutical intervention, vaccination. 1 Introduction In the mathematical theory of epidemic control it is generally assumed that social planners (e. g. governments, public health officers, etc.) choose appropri- ate strategies to fight epidemic outbreaks when they occur. It is also assumed that they have some intervention tools available, as therapeutic treatments or preventive vaccines. Then, optimal control theory may suggest the best plan for implementing such interventions to achieve the best outcome for the chosen strategy during an intervention campaign [1, 5, 27]. A common assumption in the literature is that the set of available tools remains unmodified throughout the whole campaign, from planning time to completion (see [8, 9, 26, 30, 32] for some very recent contributions). However,