In this research article, we developed and analyzed a mathematical model for studying the dynamics of homelessness in a resource-limited community. In the model, the homelessness is assumed to spread via social and neighborhood influences as well as due to demographic factors. The model, parameterized using data from the county of Los Angeles-California, is used to identify situations when two interventions, housing assistance, and job training programs, are most effective. There is a trade-off between the two choices interventions, which is a function of socio-demographic characteristics of the region.