Combining COVID-19 vaccination with social distancing measures

Abstract

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