Spatiotemporal causal inference with mechanistic ecological models: Evaluating targeted culling on chronic wasting disease dynamics in cervids

Spatiotemporal causal inference methods are needed to detect the effect of interventions on indirectly measured epidemiological outcomes that go beyond studying spatiotemporal correlations. Chronic wasting disease (CWD) causes neurological degeneration and eventual death to white-tailed deer (Odocoileus virginianus) in Wisconsin. Targeted culling involves removing deer after traditional hunting seasons in areas with high CWD prevalence. The evaluation of the causal effects of targeted culling in the spread and growth of CWD is an important unresolved research and CWD management question that can guide surveillance efforts. Reaction–diffusion partial differential equations (PDEs) can be used to mechanistically model the underlying spatiotemporal dynamics of wildlife diseases, like CWD, allowing researchers to make inference about unobserved epidemiological quantities. These models indirectly regress spatiotemporal covariates on diffusion and growth rates parameterizing such PDEs, obtaining associational conclusions. In this work we develop an innovative method to obtain causal estimators for the effect of targeted culling interventions on CWD epidemiological processes using an inverse-probability-of-treatment-weighted technique by means of marginal structural models embedded in the PDE fitting process. Additionally we establish a novel scheme for sensitivity analysis under unmeasured confounder for testing the hypothesis of a significant causal effect in the indirectly measured epidemiological outcomes. Our methods can be broadly used to study the impact of spatiotemporal interventions and treatment exposures in the epidemiological evolution of infectious diseases that can help to inform future efforts to mitigate public health implications and wildlife disease burden.