⚙️ Core: Refactor Gillespie Algorithm to Strategy Pattern

[fderuiter]

🔧 The Violation

The gillespie_step_time function in math_explorer/src/epidemiology/stochastic.rs violated several "Systems Core" principles:

1. Dependency Inversion Violation: It relied on rand::thread_rng(), making it impossible to seed for deterministic testing.
2. Open/Closed Violation: It hardcoded the logic for a 2-event system (Infection/Recovery), requiring modification to support other models (e.g., SEIR).
3. Side Effects: Implicit randomness made the function impure and hard to verify.

🛠️ The Fix

I applied the Strategy Pattern and Dependency Inversion:

1. Defined a StochasticSystem<State> trait that allows any model to define its propensities (rates) and reaction logic.
2. Implemented a generic GillespieSolver<R: Rng> that accepts any RNG strategy (e.g., StdRng, ThreadRng).
3. Implemented StochasticSystem for the existing SIRModel.
4. Deprecated the old gillespie_step_time function.

📉 Debt Reduction

• Removed implicit dependency on thread_rng.
• Decoupled the simulation algorithm (Gillespie SSA) from the specific biological model.
• Enabled future extension to other stochastic models (SEIR, Lotka-Volterra) without modifying the solver code.

🧪 Integrity

• Ran cargo test successfully.
• Added test_gillespie_solver_deterministic which verifies the solver behavior using a fixed seed, ensuring logic is preserved and correct.
• Verified SIRModel implementation matches the expected reaction dynamics.

---

PR created automatically by Jules for task 14656697529283794320 started by @fderuiter

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[fderuiter]

Run cargo fmt -- --check
Diff in /home/runner/work/math/math/math_explorer/src/epidemiology/stochastic.rs:1:
-use rand::Rng;
use crate::epidemiology::compartmental::{SIRModel, SIRState};
+use rand::Rng;

/// A trait for systems that can be simulated stochastically.
///
Diff in /home/runner/work/math/math/math_explorer/src/epidemiology/stochastic.rs:142:
/// Calculates time to next event for SIR system (Gillespie).
///
/// $\tau = - \ln(U) / (\text{rate}{infect} + \text{rate}{recover})$
-#[deprecated(since = "0.1.0", note = "Use GillespieSolver instead for full simulation")]
+#[deprecated(

• since = "0.1.0",
• note = "Use GillespieSolver instead for full simulation"
  +)]
  pub fn gillespie_step_time(rate_infect: f64, rate_recover: f64) -> f64 {
  let mut rng = rand::thread_rng();
  let u: f64 = rng.r#gen(); // Uniform (0, 1)
  Diff in /home/runner/work/math/math/math_explorer/src/epidemiology/stochastic.rs:161:
  #[cfg(test)]
  mod tests {
  use super::*;

• use rand::rngs::StdRng;
  use rand::SeedableRng;

• use rand::rngs::StdRng;

  #[test]
  fn test_extinction_probability() {
  Error: Process completed with exit code 1.

[google-labs-jules]

Run cargo fmt -- --check
Diff in /home/runner/work/math/math/math_explorer/src/epidemiology/stochastic.rs:1:
-use rand::Rng;
use crate::epidemiology::compartmental::{SIRModel, SIRState};
+use rand::Rng;

/// A trait for systems that can be simulated stochastically.
///
Diff in /home/runner/work/math/math/math_explorer/src/epidemiology/stochastic.rs:142:
/// Calculates time to next event for SIR system (Gillespie).
///
/// $\tau = - \ln(U) / (\text{rate}{infect} + \text{rate}{recover})$
-#[deprecated(since = "0.1.0", note = "Use GillespieSolver instead for full simulation")]
+#[deprecated(

• since = "0.1.0",
• note = "Use GillespieSolver instead for full simulation"
  +)]
  pub fn gillespie_step_time(rate_infect: f64, rate_recover: f64) -> f64 {
  let mut rng = rand::thread_rng();
  let u: f64 = rng.r#gen(); // Uniform (0, 1)
  Diff in /home/runner/work/math/math/math_explorer/src/epidemiology/stochastic.rs:161:
  #[cfg(test)]
  mod tests {
  use super::*;

• use rand::rngs::StdRng;
  use rand::SeedableRng;

• use rand::rngs::StdRng;

  #[test]
  fn test_extinction_probability() {
  Error: Process completed with exit code 1.

I have run cargo fmt and pushed the changes.