Optimized Scheduling of COVID-19 Testing

to protect tenants in sheltered housing and nursing homes. We consider
the challenge created by a limited budget of tests, namely, only a
fraction of the staff and tenants can be tested per day. This leads to
the question of who should be tested each day? Our goal is to
compute a daily sample limited by the test budget while maximizing the
probability of detecting an outbreak as soon as possible.

Coping with this question requires (at least) two models: a model for
the probability that individuals carry the virus and a model of
contagiousness.

We suggest a model for individuals carrying the virus that is derived
by known threats such as residence location, attendance of weddings
or bars, usage of public transportation, etc. This risk factor is
discounted by the number of days that have elapsed since the last
test.

We also suggest a model that represents potential contagions by
defining a set system that captures exposure groups such as people
that: (i) work in the same location, corridor, or department, (ii)
attend the Mensa during the same time slots, or (iii) share
transportation.

We formulated an integer linear program (ILP) that that attempts to
maximize coverage of groups in a fair manner. We implemented this ILP
so that a daily set of testees is computed. We plan to extend this
tool to compute a multi-day optimized schedule.

Joint with Konstantin Berestizshevsky and Moni Shahar