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

Source abstract

Abstract 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.