  We analyze an optimal control version of a simple SIR epidemiology model that
includes a partially specified vaccination policy and takes into account
fatigue from protracted application of social distancing measures. The model
assumes demographic (age related) categories, and is otherwise homogeneous.
Maximum capacity for vaccination is exogenous and the authorities select its
allocation to the categories. They can also adopt measures to uniformly
diminish the contact rate between infected and susceptible individuals at an
economic cost. Total or partial immunity is modeled, while the contact rate is
allowed to exhibit seasonality. We apply optimal control methods to minimize a
cost index while guaranteeing that health system capacity is not exceeded. A
reasonable parameter selection leads to policies specifying that vaccination
priority should be given to the category with a higher demand for the limited
health care resources regardless of cost variations among categories.
Vaccination priority reverses if some demographic category has significantly
higher mobility while for some parameter values vaccination alternates among
categories. Optimal social distancing policies exhibit seasonality, and hence
reducing susceptibles below the average spontaneous disease extinction level
does not necessarily lead to a repeal of social distancing.
