Limiting the spread of disease through altered migration patterns

• We examine the effect of migration patterns on the initial phase of an epidemic.
• We aim to minimise the expected growth rate and basic reproduction number.
• An explicit optimal distribution of susceptible individuals is found.
• This distribution is optimal for probability of extinction and total size of the epidemic.

We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations by the migration of infected individuals. We show how susceptible individuals can act collectively to limit the spread of disease during the initial phase of an epidemic by specifying the distribution that minimises the growth rate of the epidemic when the infectives are migrating so as to maximise the growth rate. We also give an explicit strategy that minimises the basic reproduction number, which is also shown be optimal in terms of the probability of extinction and total size of the epidemic.