Advances in ecological modelling and disease analytics

This dissertation is organized into three interrelated research streams. Computational Efficiency and Precision: We improve the computational efficiency and precision of replicated-count and batch-marked hidden population models. Efficiency is achieved by applying a Fast Fourier Transform to compute convolutions in the likelihood function. To maintain precision for large population sizes, we use the 'Log-Sum-Exp' method for summations in log-space. Additionally, we derive an approximate asymptotic solution to the N-mixtures model, significantly enhancing computational efficiency while preserving precision in large-scale population studies. Disease Analytics: We develop a new class of disease analytic models that utilize discrete counts of detected cases, deaths, and recoveries—aggregate data that can be made publicly available during a pandemic. These models estimate under-reporting rates, enabling more accurate assessments of a pandemic's true extent. Applying our models to the Northern Health Authority Region of British Columbia, we validate our models using a seroprevalence study. We further extend these models to multiple sites, distinguishing between domestic spread from symptomatic and asymptomatic cases. We use this methodology to obtain time-varying estimates of under-reporting across all provinces and territories in Canada. Ecological Modelling: We enhance batch-marking recapture methodology by improving computational tractability and eliminating the need for state binning when handling large hidden populations. This advancement improves both computational precision and efficiency, enabling more complex model structures with parameter covariates. Additionally, we develop a flexible framework for incorporating functional parameters into diverse ecological models, demonstrating that these functional models yield more precise parameter estimates than classical approaches.