Locust swarms hit subsistence-staple-crop-growing households at random and are not privately controllable. An aerial-spraying optimal control model that supports the said households' livelihood at least expected cost is therefore developed. The qualitative properties of the model are analysed under economically plausible but mild assumptions. The steady state comparative statics reveal that the locust swarm size and the probability of a household's crop being destroyed by a swarm decrease with the number of households, yield per household, and the staple crop's replacement price, and increase with the marginal cost of spraying and the planner's discount rate. A local comparative dynamics analysis is also conducted, as it provides the necessary economic intuition behind other ostensibly anomalous steady-state comparative statics results.