System Dynamics and the Hydrology of Homelessness: A Stock and Flow Analysis of the United States Crisis

The Epistemological Shift in Homelessness Analysis: From Static Counts to Complex Systems Modeling

The crisis of homelessness in the United States is frequently misunderstood through the lens of static measurements. For decades, the dominant methodologies for quantifying the unhoused population have relied on point-in-time snapshots, capturing the visible crisis on a single night but failing to illuminate the longitudinal flows that sustain it.1 However, homelessness is not a static demographic condition; it is a highly fluid, dynamic state characterized by constant movement into and out of housing instability. To accurately comprehend and ultimately resolve this crisis, policymakers and researchers must move beyond simple demographic headcounts and apply the rigorous analytical frameworks of complex systems theory and system dynamics.1

System dynamics provides a robust mathematical and conceptual architecture for evaluating coordinated responses to complex social phenomena.1 Complex systems are composed of multiple interacting agents that engage in nonlinear behaviors, constantly adapting to conditions within the system.3 These interactions generate feedback loops—mechanisms that influence future system behaviors. Reinforcing feedback loops accelerate growth (such as the compounding trauma of street homelessness leading to deeper chronicity), whereas balancing feedback loops limit growth (such as successful rapid re-housing interventions).3 Because the nature of homelessness is inherently obscure and multifaceted, utilizing system dynamics modeling frameworks—often built using simulation software like Stella Architect or Vensim—allows communities to obtain a deeper understanding of these structural elements and their emerging effects.1

In this mathematical framework, the total homeless population at any given moment is conceptualized as a “stock” (a reservoir or a lake).1 The individuals losing housing and entering the system represent the “inflows” (incoming rivers), and those securing permanent housing or self-resolving their crisis represent the “outflows” (outgoing rivers or drains).1 Mathematically, the fundamental system dynamics of homelessness can be characterized by a differential equation where the rate of change in the homeless population over time is equal to the rate of entries minus the rate of exits: d(homelessness(t))/dt = entries(t) – exits(t).3

If the inflow rate exceeds the outflow rate, the stock of homelessness accumulates. If the outflow rate is equivalent to the inflow rate, the system reaches a steady state. By definition, homelessness will functionally end in a community—reaching a state commonly referred to as “Functional Zero”—only when the sum of outflows exceeds the sum of inflows for a sustained period, thereby draining the stock to near zero.1 This goal can only be achieved through policy that triggers one of three conditions: (1) increasing the outflow rate while inflow remains unchanged, (2) reducing the inflow rate while outflow remains unchanged, or (3) concurrently increasing outflow and reducing inflow.1

When communities lack visibility into the specific dynamics of their inflows and outflows, they risk implementing counterproductive policies plagued by delayed effects, unintended tipping points, and “worse-before-better” scenarios.3 For example, in a system resembling a bathtub, if the volume of water flowing from the tap (inflow) is greater than the capacity of the open drain (outflow), the water level will continue to rise.4 A failure to simultaneously restrict the tap and widen the drain leads to systemic overflow, which in the context of homelessness, manifests as expanding unsheltered encampments and overburdened emergency shelter networks.4 System dynamics models demonstrate that attempts to solve homelessness merely by expanding emergency shelter capacity without concurrently widening permanent housing outflows creates a reinforcing loop that perpetuates the stock.4

Quantifying the Macroscopic Stock: The 2025 Baseline

To parameterize a system dynamics model, it is first necessary to establish the baseline measurements of the existing stock. The primary mechanism for this in the United States is the Annual Homeless Assessment Report (AHAR) Part 1 to Congress, which utilizes Point-in-Time (PIT) counts conducted nationwide by local Continuums of Care (CoCs) on a single night during the last 10 days of January.8 The HUD definition of “literal homelessness” utilized in this count includes individuals staying in emergency shelters, transitional housing programs, safe havens, or unsheltered locations such as cars, streets, or encampments.11 Crucially, this definition excludes the “hidden homeless”—those staying temporarily with family or friends (couch-surfing) or residing in other unstable living situations—which implies that the true stock is likely higher than official estimates.4

According to the 2025 AHAR data, an estimated 745,652 people were experiencing literal homelessness on a single night in the United States.11 This figure represents a 3% decrease from the record high of 771,480 recorded in 2024, yet it remains 27% higher than the baseline established in 2013, indicating significant long-term accumulation within the systemic stock.12

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The composition of this stock reveals critical vulnerabilities. Of the total population, 266,320 individuals were living unsheltered—residing in places not meant for human habitation.12 Unsheltered homelessness has surged by 36% since 2013, driven heavily by severe housing affordability crises, inadequate systemic outflow mechanisms in major urban centers, and the compounding effects of the 2024 migration crises that severely impacted family homelessness.12 In 2025, the decline in the national stock was largely driven by a 4% decrease in emergency shelter utilization (16,931 fewer people) and a 3% decline in unsheltered persons (7,904 fewer people) compared to 2024.13

Geographically, the stock is highly concentrated and deeply regional. California alone accounted for roughly 30% of all homeless individuals in the United States, recording a total unhoused population of 181,934 in 2025.12 While California experienced a 2.8% decrease year-over-year—its first decline since 2016—its unsheltered rates remain severe.21 In 2025, Hawaii, California, Arkansas, Arizona, and Georgia all reported that 65% or more of their homeless populations were entirely unsheltered.20 Conversely, massive regional declines were observed in states that heavily invested in coordinated housing placement systems; between 2024 and 2025, Illinois saw a 44% decrease in homelessness, Hawaii a 41% decrease, Florida an 11% decrease, and New York an 8% decrease.13

The demographic subpopulation data highlights divergent systemic pathways. The number of homeless single individuals reached a record high of 515,286 in 2025.13 In contrast, the number of people in families with children decreased by 11% from 2024 to 2025, landing at 230,366.13 Despite this recent drop, family homelessness was still 70% higher in 2025 than it was in 2013.13 New York and California maintained the highest absolute numbers of people in homeless families, with 84,923 and 26,142 people respectively.20 Additionally, while veteran homelessness dropped slightly to 32,495 in 2025 (building on massive reductions achieved since 2013 via the HUD-VASH program), the stock of chronically homeless individuals reached a record high of 155,750.13 This represents an alarming 81% increase in chronic homelessness since 2013, indicating a severe failure in the system’s ability to facilitate outflows for its most disabled constituents.12

Furthermore, to understand the true size of the systemic infrastructure supporting this population, one must recognize that the PIT count only measures the active, unresolved stock. In 2025, alongside the 745,652 people literally experiencing homelessness, there were 1,456,923 individuals living in taxpayer-subsidized or funded housing designated specifically for the homeless, such as Permanent Supportive Housing (PSH) and Rapid Re-Housing (RRH).12 These beds represent the “outgoing rivers” and subsequent permanent reservoirs of the system. Between 2013 and 2025, the number of taxpayer-funded beds increased by 151%, and Continuum of Care (CoC) spending increased by 111%.12 Yet, despite this massive expansion of outflow reservoirs, overall homelessness still increased by 27% during that same period.12 This proves definitively that merely expanding the outflow reservoirs without concurrently throttling the upstream inflow rivers is a mathematically insufficient strategy for reaching functional zero.

Beyond the Point-in-Time: The Hidden Velocity of Annual Flows

While the single-night PIT count is useful for measuring the immediate capacity burden on shelters, it vastly underestimates the true velocity and volume of the system. A stock measurement is merely a snapshot; it does not capture the thousands of individuals who enter and exit the system between January and December.

To observe this longitudinal flow, HUD publishes the AHAR Part 2 report, which tracks the annual estimate of people experiencing sheltered homelessness.25 Data from the federal fiscal year 2022 indicates that 1,388,425 people (comprising 1,066,514 households) accessed an emergency shelter, transitional housing program, or safe haven over the course of the year.25 This annual inflow is exponentially larger than the single-night snapshot. For example, while the PIT count might identify ~32,000 homeless veterans on a single night, the annual data from 2022 revealed that 85,234 veterans spent at least one night in a shelter over the year.25

This high rate of churn emphasizes why system dynamics modeling is essential. If a community identifies 1,000 homeless individuals in its PIT count, but its annual inflow is actually 4,000 people and its annual outflow is 3,900 people, the system is processing a massive volume of human traffic despite the static stock only growing by 100 individuals.28 Understanding this throughput velocity is the fundamental prerequisite for designing targeted interventions.

The Topography of Inflow: The 80-10-10 Typological Framework

To construct an accurate system dynamics model of homelessness, one must segment the incoming rivers based on the behavioral pathways and temporal patterns of the individuals entering the system. Treating the homeless population as a homogenous mass leads to misallocated resources and systemic gridlock.

The foundational paradigm for understanding these flows was established by Dennis Culhane and Randall Kuhn in their landmark 1998 empirical analysis of public shelter utilization in New York City and Philadelphia.30 By applying cluster analysis to longitudinal administrative data, they moved beyond static demographics to identify three distinct temporal typologies of homelessness: Transitional, Episodic, and Chronic.33

Crucially, Kuhn and Culhane discovered that the flow of individuals entering the homeless shelter system reliably bifurcates into an approximate 80%, 10%, and 10% split across these three typologies.30 This predictable ratio provides the precise flow parameters required to populate a systemic stock-and-flow model, demonstrating how the vast majority of individuals pass through the system quickly, while a small minority consume a disproportionate amount of systemic time and resources.

Typology PathwayPercentage of FlowFrequency of EpisodesDuration of EpisodesPrimary Systemic Characteristic
Transitional80%Low (Typically 1 or 2)Short (Days/Weeks)Rapid throughput; highly responsive to light-touch interventions and self-resolution.
Episodic10%High (Frequent cycling)Short to MediumChurning flow; cycles between shelters, streets, and institutions (jails, hospitals).
Chronic10%Low (Continuous)Long (Continuous > 1 year)Stagnant stock accumulation; requires intensive, permanent supportive interventions.

The Broad, Fast-Moving River: Transitional Homelessness (80%)

The “Transitional” demographic constitutes the overwhelming majority—80 percent—of the inflow into the homeless shelter system.30 In a system dynamics model utilizing hydrological metaphors, this represents a massive, wide incoming river. However, the defining characteristic of this group is the velocity of their throughput. Transitional homelessness is defined by low frequency and short duration; these individuals typically experience a single, brief episode of homelessness before exiting the system and not returning.30

Historically, data from New York City indicated that transitionally homeless individuals averaged only 1.4 shelter stays over a three-year period, accumulating an average total of just 58 days in the system over those three years.35 Demographically, this group tends to be younger, disproportionately Black (reflecting deeper structural inequities such as poverty and housing discrimination), and frequently driven into homelessness by acute, temporary crises such as a sudden job loss, a healthcare emergency, an eviction, or fleeing a domestic violence situation.38 In New York City and Philadelphia, individuals experiencing transitional homelessness were predominantly Black (83.6% and 90.5% respectively) and male (81.5% and 81.8%), with a large cohort under the age of 30.41 Furthermore, foster care systems act as a significant upstream tributary; approximately 31% of foster care children who age out of the system will experience transitional homelessness in their twenties.38

Because the transitional river flows so rapidly, these individuals do not accumulate heavily in the point-in-time stock despite representing 80% of the annual inflow. From a policy perspective, this population relies heavily on rapid self-resolution or light-touch interventions. Observational studies tracking the outcomes of adults entering the shelter system for the first time found that within 18 months, 81% had returned to housing.44 Current estimates suggest that approximately 35% of individuals experiencing transitional homelessness self-resolve their crisis and find housing on their own within 30 to 60 days, often moving in temporarily with family or friends.44

For those who cannot self-resolve, rapid re-housing (RRH)—an intervention providing time-limited financial assistance and targeted supportive services—is highly effective at accelerating their outflow back into permanent housing without the need for lifelong subsidies.7 Furthermore, because their episodes are precipitated by financial crises, upstream prevention strategies are mathematically proven to be highly cost-effective at damming this inflow river before the individuals ever reach the shelter system. Experimental evidence has demonstrated that families receiving proactive financial assistance had half the homelessness rate of those who did not, proving that providing a $1,000 emergency cash infusion is significantly cheaper for the taxpayer than absorbing the costs of a shelter stay.45

The Churning Rapids: Episodic Homelessness (10%)

The second incoming river, representing approximately 10% of the shelter inflow, is defined by “Episodic” homelessness.30 If transitional homelessness is a fast-moving, straight river, episodic homelessness functions as a series of churning rapids characterized by cyclical eddies and whirlpools within the system dynamics model.

Episodic homelessness is structurally defined by high frequency but relatively short individual durations.31 These individuals move in and out of the shelter system on a regular, repeating basis, often alternating between public shelters, temporary accommodations, the streets, and costly institutional settings like jails, hospitals, and inpatient treatment centers.33 In the original Kuhn and Culhane dataset for New York City, episodically homeless individuals experienced an average of 4.9 distinct shelter episodes over a three-year period, spending a cumulative 264 days in the system with an average single length of stay of 54.4 days.35

Demographically, episodic users share similarities with the transitional group—they tend to be younger individuals (often under 30) and are predominantly Black (over 90% in cities like Philadelphia)—but they are frequently burdened by emerging chronic addictions, untreated mental illnesses, or complex behavioral health challenges.34 Among families, those with episodic patterns of repeat stays often exhibit the highest rates of intensive behavioral health treatment, unemployment, and placement of children in the foster care system.40

In a system dynamics model, the episodic river creates severe nonlinear disruptions. The constant cyclical flow artificially inflates demand at intake points and creates immense friction across multiple municipal sectors, transferring the cost of homelessness to the healthcare and criminal justice systems.33 Arrests, hospital discharges, and parole violations continually feed the episodic loop back into the streets.47 Breaking this cycle requires coordinated discharge planning to ensure that individuals leaving mainstream programs do not flow directly back into the homelessness stock.34

The Deep, Stagnant Lake: Chronic Homelessness (10%)

The final 10% of the system’s inflow feeds into the “Chronic” homelessness typology.30 While this group represents the smallest volume of incoming flow, their lack of systemic exit velocity means they pool together, forming a deep, stagnant lake that dominates the static point-in-time stock and consumes the vast majority of systemic resources.

Chronic homelessness is officially defined by HUD as a pattern of continuous stay in shelters or on the streets extending over a year or more, or at least four episodes of homelessness in the past three years, coupled with a disabling condition.31 While they make up only 10% of the annual inflow, prior studies (such as Culhane and Kuhn’s work) demonstrated that chronically homeless adults can consume upwards of 18% to 50% of total shelter days, effectively spending every single night in the system.30

The demographics of the chronic lake skew older, and the population is characterized by profound, disabling vulnerabilities.34 A recent study found that nearly half of all single homeless adults in California are 50 or older, representing an aging cohort that is increasingly trapped in the chronic stock.42 Furthermore, among people enrolled in programs addressing chronic homelessness, roughly 50% are African American, underscoring the compounding intersectionality of race, age, and disability.41

Because the outflow rate for the chronic lake is naturally near-zero—these individuals are largely incapable of self-resolving their homelessness—the only viable systemic intervention to drain this stock is Permanent Supportive Housing (PSH).7 System planners must be alerted to patterns of extended stays so that individuals failing to exit the transitional river can be quickly identified and diverted into PSH before they permanently settle into the chronic lake.34 The recent 81% surge in chronic homelessness between 2013 and 2025 (reaching 155,750 individuals) is a direct mathematical consequence of inflow rates outpacing the creation of new PSH units.13

Addiction and Behavioral Health as Flow Regulators

To accurately model the complex dynamics of the homelessness system, it is necessary to build a distinct sub-system representing substance abuse and behavioral health disorders. These conditions act as powerful flow regulators, acting as strict choke-points that effectively block the outgoing rivers and prevent individuals from transitioning back into stable housing.

The incidence of psychiatric and substance use disorders is vastly greater among the chronically homeless than among the transitional or episodic populations.48 Analyses of data from the National Survey of Homeless Assistance Providers and Clients (NSHAPC) show that over 60% of people experiencing chronic homelessness have experienced lifetime mental health problems, and over 80% have experienced lifetime alcohol and/or drug problems.41 Among the contemporary chronic population, current estimates suggest that about 30% suffer from active mental health conditions, and approximately 50% have co-occurring substance use problems.41

In a comprehensive stock-and-flow model, such as the one developed by researchers to analyze homelessness in California using Stella Architect, the unsheltered population is further segmented by addiction status.5 Empirical data indicates that approximately 30% of all individuals living entirely unsheltered suffer from active substance abuse disorders.41 This creates a massive secondary flow from the general stock of “People Unsheltered” into a highly vulnerable sub-stock of “Unsheltered People Abusing Substances”.49

Once trapped in this sub-stock, an individual’s probability of exiting the system via self-resolution plummets. The mathematical flow dictates that a percentage of these individuals must either achieve sobriety independently or secure access to specialized treatment to flow back into the general unsheltered or sheltered stocks, and from there, attempt to flow into permanent housing.49 However, because the friction coefficient preventing outflow is immense, this group requires integrated behavioral healthcare directly tied to housing interventions.

Furthermore, the harsh realities of unsheltered life function as a reinforcing feedback loop within the system dynamics. The model formulates “unsheltered life” as a stock whose severity gradually rises over time.49 As the trauma of street homelessness deepens, mental health inevitably deteriorates, and substance use frequently becomes a coping mechanism for the physical and psychological toll of exposure, violence, and sleep deprivation. Therefore, prolonged time spent in the “stock” actually degrades the individual’s capacity to access the “outflow,” necessitating increasingly intensive and expensive interventions (like PSH) to achieve system exit.

The Economics of the Lake: Cost Analysis of Stagnant Stocks

Maintaining a stagnant stock of chronic homelessness is not only a policy failure; it is an economic catastrophe. System dynamics modeling proves that allowing individuals to pool in the chronic lake exponentially increases municipal expenditures across disconnected mainstream systems.

The landmark 2002 “Culhane Report” quantified these systemic externalities by tracking the public service utilization of 4,679 homeless, mentally ill residents in New York City from 1989 to 1997.50 The analysis revealed the exorbitant “cost of doing nothing.” By comparing the service utilization of homeless individuals to housed individuals, Culhane demonstrated that a chronically homeless, mentally ill person living on the streets cost taxpayers an average of $40,451 annually (in 1999 dollars).50 These costs are driven almost entirely by the highest-friction emergency interventions: psychiatric inpatient care, emergency room visits, and cyclical incarcerations.50 Costs spike substantially immediately before first-time homelessness and peak during the period just after an individual enters the residential homeless system.34

Housing StatusAnnual Public Service Cost per Individual (1999 Dollars)Primary Cost DriversNet Economic Impact of Intervention
Chronically Homeless (Street/Shelter)$40,451Psychiatric inpatient care, Emergency room visits, Incarceration, Emergency ShelterN/A (Baseline cost of maintaining stagnant stock)
Housed in Permanent Supportive Housing (PSH)$24,169Subsidized lease, On-site wraparound behavioral health services, Case management$16,282 Net Savings per unit

The Culhane Report revolutionized homelessness policy by proving that placing these individuals in supportive housing reduced systemic costs by a net $16,282 per unit annually.50 Providing a permanent home with wraparound services is mathematically cheaper than funding the chaotic, cyclical use of emergency systems. Therefore, draining the chronic lake via Permanent Supportive Housing is not merely a humanitarian imperative, but a fiscally superior strategy that pays dividends back into the municipal budget.50

The Outgoing Rivers: System Exits and Outflow Infrastructure

The final component required to model the system dynamics of homelessness involves mapping and quantifying the outgoing rivers. If a community wishes to lower the water level in its systemic bathtub, it must deeply understand the capacity, flow rate, and destination of its drains.4 Cross-sector programs developed through initiatives like the Healthcare and Homelessness pilot explicitly aim to increase this outflow by building codifiable pathways out of the system.52

The primary pathways out of the homelessness stock can be categorized as either spontaneous self-resolution or system-facilitated housing placements. As previously noted, self-resolution accounts for a massive portion of the transitional 80% outflow, with individuals naturally exiting to family or market-rate housing.44

However, for the remaining populations, the system must engineer artificial outgoing rivers through heavily funded housing interventions. These interventions fall into three primary categories, tracked annually by HUD’s Housing Inventory Count (HIC) 8:

  1. Transitional Housing (TH): Temporary housing with supportive services aimed at stabilizing individuals for up to 24 months before they transition to permanent housing.7
  2. Rapid Re-Housing (RRH): An intervention informed by the “Housing First” methodology, RRH provides short-term financial assistance (first and last month’s rent, security deposits) to quickly push individuals out of the system before they lose their economic footing.7
  3. Permanent Supportive Housing (PSH): The sole viable outflow river for the chronically homeless. PSH combines long-term leasing assistance with intensive, mandatory support services for individuals with severe disabilities.7

In 2024, Rapid Rehousing, Permanent Supportive Housing, and Other Permanent Housing (OPH) programs constituted 57% of all beds reported in the national housing inventory.8 Between 2023 and 2024, the total inventory for these permanent programs increased by 3%, with OPH seeing the largest jump (14,735 more beds).8

However, a critical system dynamics constraint exists within the PSH model: because PSH is permanent, the “flow rate” through these units is extremely slow. Unlike an emergency shelter bed that might host 10 different people over a year (high flow), a PSH bed hosts the same individual for years or decades (low flow, high stock accumulation).4 Transition rates out of PSH back into general, unsubsidized housing are low, though some models assume average lengths of stay around 3.5 years.4 Therefore, to maintain a functional system, continuous capital investment in new PSH stock is required just to keep the outflow river moving, making it vital to correctly identify who requires PSH and who can be served by the faster-flowing RRH river.7

Reaching Functional Zero: Calibrating the Hydrology

The ultimate objective of applying system dynamics to homelessness is to engineer a system that achieves “Functional Zero.” This is not a static state where homelessness literally never occurs; rather, it is a dynamic equilibrium where the system’s capacity to process and house individuals outpaces the rate at which people lose their housing.1

In advanced system modeling utilized by Continuums of Care (CoCs) nationwide, Functional Zero is mathematically operationalized by two primary criteria 7:

  1. The annual outflow (people housed) must be greater than or equal to the annual inflow (people becoming homeless).
  2. The total unmet need (the existing stock) must be less than or equal to 50% of the annual outflow.

When these conditions are met, the system achieves equilibrium, and the average length of time an individual spends in the system of care drops to roughly 45 days.7 Achieving this requires meticulous tracking of local data. For example, in Savannah (Chatham County), strategic planners identified an expected annual inflow of 85 individuals, accounting for an influx of populations migrating from outside the county.55 By assuming that 40% of inflows would self-resolve within 12 months, and 20% of the total shelter population would transition back into housing, they calculated an estimated annual outflow of 150.55 Because their projected outflow (150) exceeded their inflow (85), they established a mathematically viable pathway to Functional Zero.55 Similarly, in Springfield, the annual inflow to the local homeless system was 746 people, but the outflow was only 591 people, resulting in a continuous annual accumulation that required a strategic plan to build 765 new housing units to balance the equation.28

Ultimately, homelessness is not an intractable, ambient condition of urban life; it is a measurable, mathematically definable systems engineering failure. By embracing the stock-and-flow logic of system dynamics—acknowledging the rapid throughput of the 80% transitional population, the turbulent cycling of the 10% episodic demographic, and the severe, accumulating stagnation of the 10% chronic subset—policymakers can move beyond reactive crisis management. Throttling the incoming rivers through targeted prevention and radically widening the outgoing rivers via Permanent Supportive Housing and Rapid Rehousing provides the only empirical pathway to engineering the end of homelessness.

System Dynamics Diagram of Homelessness in the United States (Stocks & Flows)

image

Works cited

This report was generated by Google Gemini Deep Research using the prompt:

“You are an expert on homelessness in the United States. Research data that would enable someone to model the stock and flows of homelessness incoming rivers with lakes with outgoing rivers. Provide statistics to enable populating this diagram. The incoming rivers should be the standard 10/10/80% split of the flow of the homeless.”

Then to generate the diagram, attaching the above report and used the following prompt: “Use data from the attached to generate a diagram of the stocks and flows of homelessness in the united states in the form of incoming and outgoing rivers from a lake”

It was reviewed by Dr. Andrew Sears for accuracy.

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