Guidelines for the prioritization of adoptable shelter animals for sterilization to reduce average length of stay: a mathematical model.

OBJECTIVE: To determine the prioritization of shelter animals for sterilization surgery based on length of stay (LOS), when animals must be sterilized before adoption but capacity constraints necessitate deferral. METHODS: This mathematical modeling study defines optimal policy as prioritizing animals whose deferral would have the largest adverse impact on LOS. It derives closed-form expressions for that impact dependent on each animal's baseline (sterilized) expected LOS, adopter aversion to waiting for surgery, and deferral duration. RESULTS: Analytical derivation shows the LOS impact is monotonic in each animal's baseline LOS. Monotonicity direction depends on a parameter V measuring adoption opportunity within the deferral window. The parameter V equals the fraction of adopters willing to commit before sterilization multiplied by the duration of the deferral. An existing guideline prioritizing fast-track animals, which have shorter baseline LOS, is confirmed when V > 1. This effect is concentrated at low to medium baseline LOS (but flattens above 20 days). When V = 1, the impact becomes independent of the animal's baseline LOS. When V < 1, animals with longer baseline LOS should be prioritized, but this preference is weak. CONCLUSIONS: In practice, shelters should prioritize animals with lower baseline LOS when V substantially exceeds 1, and there are candidates with low to medium LOS. In the remaining cases, the effect is weak (including V < 1 when the direction changes), and shelters may rely on other considerations. CLINICAL RELEVANCE: These findings provide a quantitative basis for allocating limited shelter resources toward reducing LOS and shelter census, in the interest of maintaining and improving care.