SD Example 1

Exponential Growth

Population or virus spread: a single reinforcing loop drives unlimited growth until external constraints appear.

STOCK-FLOW DIAGRAM Population stock (persons) ∼ births f_r Equations: births = Population × fertility_rate d(Population)/dt = births Solution: Population(t) = Population(0) × exp(fertility_rate × t) R1 Reinforcing Loop: Population ↑ → births ↑ → Population ↑ Dynamic Behavior: • Mode: Exponential growth without bound • Doubling time: ln(2) / fertility_rate ≈ 69.3 / fertility_rate (%) years • Real-world constraint: At some carrying capacity K, births decrease (births → births × (1 − Population/K)) • Result: Logistic growth (S-curve), not exponential forever

STOCK

Population

The accumulator. Increases each time step by births. Units: persons. Initial value: 1000.

FLOW

Births

The rate. Equation: Population × fertility_rate. Units: persons/year. Positive inflow.

PARAMETER

Fertility Rate

  • Default: 0.05 (5% per year)
  • Range: 0.01–0.15
  • Effect: Controls doubling time

PATTERN

Baseline Model

Simplest possible model. One stock, one inflow, no outflow. Shows the pure J-curve. Real world adds death rates, migration, resource limits.