Current and reoccurring viral epidemic outbreaks such as those caused by the Zika virus illustrate the need for rapid development of antivirals. Such development would be facilitated by computational approaches that can provide experimentally testable predictions for possible antiviral strategies. To this end, we focus here on the fact that viruses are directly dependent on their host metabolism for reproduction. We develop a stoichiometric, genome-scale metabolic model that integrates human macrophage cell metabolism with the biochemical demands arising from virus production and use it to determine the virus impact on host metabolism and vice versa. While this approach applies to any host-virus pair, we first apply it to currently epidemic viruses Chikungunya, Dengue and Zika in this study. We find that each of these viruses causes specific alterations in the host metabolic flux towards fulfilling their biochemical demands as predicted by their genome and capsid structure. Subsequent analysis of this integrated model allows us to predict a set of host reactions, which, when constrained, inhibit virus production. We show that this prediction recovers known targets of existing antiviral drugs, specifically those targeting nucleotide production, while highlighting a set of hitherto unexplored reactions involving both amino acid and nucleotide metabolic pathways, with either broad or virus-specific antiviral potential. Thus, this computational approach allows rapid generation of experimentally testable hypotheses for novel antiviral targets within a host.