  We model the impact of local vaccine mandates on the spread of
vaccine-preventable infectious diseases, which in the absence of vaccines will
mainly affect children. Examples of such diseases are measles, rubella, mumps
and pertussis. To model the spread of the pathogen, we use a stochastic SIR
(Susceptible, Infectious, Recovered) model with two levels of mixing in a
closed population, often referred to as the household model. In this model
individuals make local contacts within a specific small subgroup of the
population (e.g.\ within a household or a school class), while they also make
global contacts with random people in the population at a much lower rate than
the rate of local contacts.
  We consider what happens if schools are given freedom to impose vaccine
mandates on all of their pupils, except for the pupils that are exempt from
vaccination because of medical reasons. We investigate how such a mandate
affects the probability of an outbreak of a disease and the probability that a
pupil that is medically exempt from vaccination, gets infected during an
outbreak. We show that if the population vaccine coverage is close to the
herd-immunity level then both probabilities may increase if local vaccine
mandates are implemented. This is caused by unvaccinated pupils moving to
schools without mandates.
