Using Markov Modeling to Understand the Dynamics of Unhoused Populations Experiencing Serious Mental Illness

The authors aimed to develop a model of housing interventions that accounted for the dynamic nature of homelessness (i.e., movement into and out of housing) among an unsheltered population experiencing serious mental illness.

A four-state Markov model of housing situations among adults experiencing serious mental illness in New York City was created and was used with data from the U.S. census and U.S. Department of Housing and Urban Development. Transition probabilities used in the model were based on prior studies. After calibration to steady-state (point prevalence) population estimates, the model was used to predict the effects of adding supportive housing and other housing retention interventions.

In the base case, the population with serious mental illness and at risk for homelessness was divided among those housed, living in shelters, and experiencing chronic unsheltered homelessness. Adding approximately 2,000 units of supportive housing targeted to the chronically unsheltered population (N=2,497) reduced the size of this group by about 1,000. Supplementing this housing with retention interventions had only modest effects. Key factors driving the results were the rates at which individuals transitioned into and out of chronic unsheltered homelessness (including through institutionalization and death).

Modest transition rates into and out of chronic unsheltered homelessness meant that, although provision of supportive housing helped vulnerable people, achieving a given absolute reduction in the chronic unsheltered census required substantially more housing units than the size of the steady-state reduction. The dynamics of homeless populations complicate policy making regarding unhoused people experiencing serious mental illness.