Where the curve goes if nothing changes

The two models we use

Linear trend (default)

Projection(t) = a + b · t

where t = 0 for 2020, t = 1 for 2021, ..., t = 5 for 2025
fit a, b via least squares on 2020-2025 data
plug t = 6 (2026), 7 (2027), ..., 10 (2030)

Use this for stable-trending metrics: arrests, jail population, total 911 calls, IDOC releases.

Exponential trend (volatile metrics)

Metric(t) ~ A · e^(k · t)

log-transform to linear:
ln(Metric) = ln(A) + k · t

fit ln(A) and k on 2020-2025
exponentiate for 2026-2030

Use this for fast-moving metrics: fentanyl-involved share (rising), overdose deaths in hot-spot counties (post-pandemic spike), naloxone administrations (rising as supply expands).

Projected: overdose deaths per 100k (illustrative)

This table illustrates the shape of a projection if recent trends continue unchecked. The anchor column shows the finalized 2023 per-100k rate from the IDOH 2023 report (the same values on the Counties page); the slopes are illustrative placeholders. Re-fit with your own multi-year series for site-specific projections.

Anchors are the finalized 2023 county per-100k rates (IDOH 2023 Fatal Overdose & Suicide Report). Slopes and projected years are illustrative model output, not observed data — re-fit with a full multi-year series before relying on them.

Projected: fentanyl-involved share of overdose deaths

Indiana 2023 baseline: 51% of drug-overdose deaths involved fentanyl. Without a ceiling-cap, exponential extrapolation would put the share above 100% by 2028 — impossible. Use a logistic curve with asymptote at ~88%.

logistic(t) = L / (1 + e^(-k · (t - t0)))

where:
  L  = 88 (% asymptote)
  k  = growth-rate parameter (fit from 2020-2025 share)
  t0 = inflection year (typically ~2022 for fentanyl)

Read with caution — if a non-fentanyl synthetic opioid (nitazenes, etc.) becomes dominant, the “fentanyl share” metric stops being meaningful and the underlying “deaths” curve becomes the load-bearing one.

Projected: IDOC releases by county of admission (per 1,000)

IDOC’s “Adult Releases” tables drive this column. Pull 2020–2025 releases from each Jackson-area county, divide by population, fit linear:

releases_per_1k(t) = a + b · t

where t = 0 for 2020, ..., t = 5 for 2025

Annualization assumes Oct 2024 is approximately representative of monthly average (release rate × 12 / pop × 1000). Source: IDOC Oct 2024 Statistical Report Table 24.

Program-participation projection (rehab/reentry/MAT)

For each named program in the Counties — Programs table, track annual clients served. Fit linear growth, sum across counties:

total_program_capacity(t) = sum_over_programs( a_p + b_p · t )

Most rural-Indiana SUD and reentry programs are growing slowly (a few percent per year); some are plateauing as funding caps. Pair this projection against the projected overdose curve to surface the treatment gap: how many overdose-death equivalents are absorbed (or not) by the program-side capacity.

Recommended Python implementation

import numpy as np

def fit_linear(years, values):
    """Returns (a, b) where projection(t) = a + b*t, t = year - years[0]."""
    t = np.array(years) - years[0]
    y = np.array(values, dtype=float)
    b, a = np.polyfit(t, y, 1)
    return a, b

def fit_exp(years, values):
    """Returns (A, k) where projection(t) = A * exp(k*t)."""
    t = np.array(years) - years[0]
    y = np.log(np.array(values, dtype=float))
    k, lnA = np.polyfit(t, y, 1)
    return float(np.exp(lnA)), float(k)

def fit_logistic(years, values, L=88.0):
    """Fit logistic with fixed asymptote L (default 88%) for fentanyl share."""
    from scipy.optimize import curve_fit
    t = np.array(years) - years[0]
    y = np.array(values, dtype=float)
    def f(t, k, t0):  return L / (1 + np.exp(-k * (t - t0)))
    (k, t0), _ = curve_fit(f, t, y, p0=[0.6, 2.0])
    return L, k, t0