Residents of the D.C. homeless shelter on the site of the former D.C. General hospital. (Michael S. Williamson/The Washington Post)

The District is full of examples of how the system is failing residents.

Last summer, The Post chronicled the story of Alfred Postell, a Harvard Law School classmate of Chief Justice John G. Roberts Jr. who experienced undiagnosed mental illness for years and ended up living on the streets. But that notoriety did not translate into more funding to address the problem.

More common are stories like that of Karl, who was referred to my agency, Green Door Behavioral Health, just before his release from the D.C. Jail. Green Door helped him find and furnish an apartment, and he recently slept in his own bed for the first time in 15 years. Karl has a stable home life and a supportive network around him, and that is a better predictor for his future than being in and out of shelters. It’s also less expensive for the community.

The proposed budget from D.C. Mayor Muriel E. Bowser (D) includes a much-needed $100 million investment in affordable housing. And Bowser recently unveiled a 30-year, $660 million plan to provide new shelters for homeless families.

But Bowser’s budget falls significantly short in addressing root causes of homelessness in the District: mental-health issues and substance abuse.

The 2017 budget for the Department of Behavioral Health, the agency that funds and regulates provider organizations, including Green Door, is essentially flat, resulting in a Band-Aid approach to problems that could be solved: ending homelessness, reducing incarceration rates, controlling health-care spending and closing the achievement gap in schools.

People with persistent mental illness and substance-use disorders make up a disproportionately high percentage of the District’s homeless population. These are the people you probably think of when someone says “homeless.”

Green Door’s evidence-based programs move people off the streets and help them live productive lives despite being burdened with brain-based illnesses. But these programs need a baseline of funding that accommodates changes in care and costs that rise approximately 3 percent every year. Current rates are based on 2012 costs.

Thanks to a federal Medicaid match, an additional investment of $1.25 million from the District would put about $4 million in the hands of providers to serve District consumers. These dollars are spent on front-line services that take people off the streets and get them the help they need. An appropriate solution would tie reimbursement rates to inflation.

The D.C. Council has been addressing mental-health issues in recent years, and that’s encouraging.

Also helpful is that the District recently received a $5.5 million, three-year federal grant to increase outreach and engage chronically homeless individuals. One successful model is Housing First, which is based on ordinary requirements of tenancy, such as paying rent and fulfilling standard lease terms, rather than participation in treatment. Research shows that people get better and accept recommended treatment sooner once housed, as opposed to making housing contingent on mandated treatment participation. In concert with supportive community service programs, the Housing First model has a phenomenal success rate. Lamp Community in Los Angeles reports that 95 percent of its clients stay housed for one year or more, and that is less expensive than incarceration or homelessness.

Additionally, the District participates in the Medicaid Health Homes program, a provision of the Affordable Care Act. The District’s program is designed to improve health outcomes by increasing the coordination of health care for people with serious mental illness, who nationally have a life expectancy 14 to 32 years shorter than other Americans. Successfully implemented, Health Homes will provide another lifeline for those who have been shuffled through the system in the past.

Those living with persistent mental-health issues and substance-use disorders face daily challenges many of us could never imagine. As Bowser, the D.C. Council and the community work toward long-term solutions for the District’s homeless, they need to remember that housing the mentally ill sets off a chain reaction of positive developments by helping them become productive, tax-paying citizens.

Housing this population now is an investment today with a real bottom-line impact tomorrow.

The writer is chief executive of Green Door Behavioral Health.