Mock M3 · Spotted Lanternfly Containment Strategy

Population dynamics Spatial spread Optimization

The problem

The spotted lanternfly (Lycorma delicatula) is an invasive planthopper that has spread rapidly across the US Northeast since first detected in Pennsylvania in 2014. It threatens agriculture (especially vineyards, orchards, and hardwood timber). The Pennsylvania Department of Agriculture has asked your team to design a quantitative containment strategy.

Requirements

Build a population model for a single, isolated infestation. Include life stages (egg, instars I–IV, adult), seasonality, and reproduction. Calibrate to published reproduction rates.
Extend to spatial spread across a county-sized region (e.g., 1000 km²). Include both natural dispersal (adult flight, walking nymphs) and human-assisted spread (egg masses on vehicles).
Model three containment interventions:
- Tree-of-heaven (host) removal in the highest-density 10% of the county.
- Insecticide spraying targeting adult populations in months 6–8 of the year.
- Quarantine zone / vehicle inspections on the boundary of the infested area.
For each intervention, estimate effectiveness (% population reduction in 3 years) and cost. Identify the most cost-effective combination subject to a $5M annual budget.
Sensitivity analysis on the most uncertain parameters (reproductive rate, dispersal kernel, intervention efficacy).
One-page memo to the PA Secretary of Agriculture with your recommended budget allocation.

Useful starting data

Female lanternfly lays 30–50 eggs per egg mass; 1–2 egg masses per season.
Adult flight range: ~50–150 m per day (passive); much further via wind / vehicles.
Detection survey cost: ~$20/acre/year.
Targeted insecticide treatment: ~$60/tree, ~10 trees/acre for tree-of-heaven stands.
Mature tree-of-heaven removal: ~$300/tree.
Vehicle inspection station: ~$0.5M/year operating cost, intercepts an estimated 60–80% of passing infested vehicles.

Solution sketch

Population model

Discrete-time stage-structured Leslie matrix model with monthly time-step. State vector $\mathbf{n}(t) = (n_{\text{egg}}, n_{I}, n_{II}, n_{III}, n_{IV}, n_{\text{adult}})^\top$. Transition matrix $A(t)$ varies by month (eggs hatch in spring, adults appear midsummer, lay eggs in fall, die by winter). Reproduction: $n_{\text{egg}}(t+1) \mathrel{+}= R \cdot n_{\text{adult}}(t)$ in October.

Spatial model

Reaction–diffusion PDE for adult-density $u(x, y, t)$:

$\dfrac{\partial u}{\partial t} = D_{\text{nat}}\nabla^2 u + g(u) - m(x, y, t) \cdot u + S_{\text{human}}(x, y, t)$

$D_{\text{nat}}$ captures natural dispersal; $g(u)$ is reproductive growth; $m$ is mortality (modified by interventions); $S_{\text{human}}$ is human-mediated stochastic introductions (model as Poisson events at hot spots like trucking corridors).

Solve on a 100×100 grid with finite differences and explicit Euler steps.

Interventions as model modifiers

Intervention	Effect in the model	Cost
Host removal	Reduces $g(u)$ by 30–50% in treated cells (tree-of-heaven is preferred host)	~$300/tree × 5,000 trees = $1.5M
Insecticide	Adds mortality term $m$ during weeks 24–32	~$0.6/m² × 10% area = $600k
Quarantine	Reduces $S_{\text{human}}$ flux by 60–80% across the boundary	$0.5M / station × 4 stations = $2M

Cost-effective combination

Formulate as a knapsack with $5M budget. Plausible result: a mix of host removal (~$1.5M) plus 2 quarantine stations on the main corridors (~$1M) plus targeted insecticide in highest-density cells (~$1M) leaves $1.5M for surveillance. Total: ~70–80% population reduction at 3 years vs. the no-action baseline.

Sensitivity

The dominant unknowns are (a) the reproductive rate $R$ and (b) the dispersal coefficient $D_{\text{nat}}$. Vary each by ±40% and re-rank intervention bundles. The recommendation is typically robust to $R$ uncertainty but sensitive to $D_{\text{nat}}$ — if dispersal is much wider than expected, quarantine becomes much less effective and tree removal becomes the dominant lever.

Self-grading focus

Did you actually model life stages, not just total population?
Is your spatial model on an actual map / grid, or just a vague "spreads"?
Did you tie each intervention to a specific term in the model?
Is the budget allocation a real optimization, or just a guess?

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