The paper describes a method to understand time required to vaccinate against viruses in total as well as subpopulations. As a demonstration, a model based estimate for time required to vaccinate H1N1 in India, given its administrative difficulties is provided. We have proved novel theorems for the time functions defined in the paper. Such results are useful in planning for future epidemics. The number of days required to vaccinate entire high risk population in three subpopulations (villages, tehsils and towns) are noted to be 84, 89 and 88 respectively. There exists state wise disparities in the health infrastructure and capacities to deliver vaccines and hence national estimates need to be re-evaluated based on individual performances in the states.Comment: 14 pages, 1 Table, 5 Figures (A preliminary draft
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