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Case study

A worked accessibility analysis for a small synthetic county: five residential neighborhoods (with populations) and three clinics (with bed capacities). We compute, for each neighborhood, how many clinic beds are accessible per 1,000 residents under distance decay — the same computation SDC health-access pipelines run at full scale, here on data small enough to read.

Setup

pip install sdc-catchment

import numpy as np
import pandas as pd
from sdc_catchment import catchment_ratio, euclidean_cost

Computing accessibility

# 5 demand neighborhoods (population) and 3 clinics (capacity, beds).
demand = pd.DataFrame({
    "geoid": ["n1", "n2", "n3", "n4", "n5"],
    "value": [1200.0, 800.0, 1500.0, 600.0, 2000.0],
})
demand_xy = np.array([[0, 0], [3, 1], [6, 0], [1, 4], [5, 5]], dtype=float)
clinics = pd.DataFrame({"geoid": ["A", "B", "C"], "value": [20.0, 15.0, 30.0]})
clinics_xy = np.array([[1, 1], [5, 1], [4, 5]], dtype=float)

cost = euclidean_cost(demand_xy, clinics_xy)
# E2SFCA-style: gaussian decay within a 4-unit travel bound.
access = catchment_ratio(demand, clinics, cost, weight="gaussian", scale=2.0, max_cost=4.0)
result = demand.assign(access_per_1000=(access.values * 1000).round(3))
print(result.to_string(index=False))

geoid  value  access_per_1000
   n1 1200.0            9.647
   n2  800.0           12.242
   n3 1500.0            6.071
   n4  600.0            8.459
   n5 2000.0           14.724

Interpreting the result

The score is beds accessible per 1,000 residents, after discounting each clinic's capacity by travel distance (gaussian decay) and ignoring clinics beyond the 4-unit bound.

  • n5 is best served (14.7) — it sits right next to clinic C, the largest (30 beds), so even its big population is well covered.
  • n3 is worst served (6.1) — it's in the far corner [6, 0], distant from all three clinics, while carrying a large population (1,500). This is the neighborhood a planner would flag.
  • n2 (12.2) benefits from sitting between clinics A and B; n1 (9.6) and n4 (8.5) are moderate — near one clinic but not the largest.

Changing the kernel (weight=), its scale, or the max_cost bound shifts these scores: a wider bound or gentler decay raises access for the peripheral neighborhoods like n3.

See also