Mathematical Modelling of Homeless Population

A simple model is proposed for the changes in numbers of homeless households, of those of people housed in the private sector and of those resident in council housing. The model, which applies to a single local authority, is analysed to see how changing priorities can affect waiting times and the size of the waiting list for council accommodation. The analysis shows that, if the number of homeless is reasonably small, then altering the priority given to them makes little difference to the waiting times for other members of the population. However, lowering the priority given to rehousing the homeless significantly increases the time which they have to wait. Time scales which appear in the model indicate that the determination of steady states will not always suffice to predict the sizes of waiting lists over times of practical interest. A possible sensitive dependence on the amount of housing stock is also found.