Optimal risk-based allocation of disease surveillance effort for clustered disease outbreaks

Designing a disease surveillance program to detect a disease is challenging when animals are organized into herds, in part because disease cases are likely to be clustered. Clustered diseases are often surveilled using twostage sampling, which allocates tests both among herds and within herds. Finding the optimal allocation of tests is computationally difficult, so some surveillance programs simply seek an approximate solution. We developed a search algorithm to find the optimal allocation of tests by iteratively searching for adjustments to the test allocation that yielded marginal improvements in system sensitivity. We digitally generated 21 herds of various sizes, evenly divided among three regions that differed in relative risk. We then analyzed 29 scenarios that differed in disease and testing characteristics. We also analyzed a Chronic Wasting Disease (CWD) surveillance effort for 23 elk game management units of various sizes that were spread across three regions in Arizona, USA. We compared our marginal sensitivity approach to two other strategies for approximating the optimal distribution of tests: allocating the same number of tests to all herds selected for testing, and allocating tests so that all herds selected for testing achieve the same sensitivity. Across analysis scenarios, we found that low prevalence, high relative risk, a small budget, or high overhead costs were best addressed by concentrating tests in large, high-risk herds. When we expect multiple herds to be infected, the optimal allocation of tests depended on how we expected the cases to be distributed. Across the analyzed scenarios, our marginal sensitivity approach was most efficient, with alternative strategies requiring 0-228 % more tests to achieve the same sensitivity. For CWD in Arizona, we found the potential to double system sensitivity, given a population design prevalence of 0.16 %, from 35.8 % to 70.5 %, although social and budgetary considerations would likely constrain changes to the current allocation of tests. The marginal sensitivity approach we developed has the potential to improve disease surveillance, especially when a population includes a limited number of herds that differ in size. An important limitation of our approach is that computer runtimes could become unacceptably long for a population with many herds.