  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.
