Intervention optimisation
Intervention optimisation chooses the timing, intensity or allocation of an intervention to achieve a defined objective subject to constraints.
Let \(u(t)\) represent an intervention. A general objective may be
\[\min_u J(u)=\int_0^T\left[C_{\mathrm{bio}}(x(t))+C_{\mathrm{int}}(u(t))\right]dt,\]subject to the biological model governing \(x(t)\).
Trade-offs
Strong interventions may reduce disease or ecological damage but carry financial, social or biological costs. Optimisation makes the chosen trade-off explicit.
Robustness
An optimum based on one uncertain parameter set may perform poorly if reality differs. Robust or stochastic optimisation can account for uncertainty.
Key idea. Optimisation requires both a model of the biological system and an explicit definition of what counts as a good decision.