Simple criteria for finding (nearly) optimal vaccination strategies

Strategies for best controlling the spread of the diseases with limited vaccine available are explored. I use influenza as a representative disease in point. The model describes the dynamics of influenza spread among multiple groups that have different risks and activity levels. I define a core group consisting of individuals with occupations that brings them in contact with many other people in a day. These occupations may include service industries, teachers, health care, and government workers, to name a few. High-risk individuals are those as typically designated for: children under 5 and adults over 50, people with weakened immune systems as well as emergency and health care personnel. Under certain conditions, shifting vaccination resources away from the high-risk group to the high-activity group will result in improved herd immunity in both the high-risk group and the population as whole. This results in more high-risk people protected even though less of them are being vaccinated, with the obvious implications that current vaccination policies may be far less then optimal. I show that the criteria for the optimal strategy can be derived from simple expressions gleaned from the expression for the basic reproductive number.