A multivariate poisson integer-valued autoregressive model for public health surveillance.

This dissertation develops a first-order multivariate Poisson integer-valued autoregressive (MPINAR(1)) model to improve disease outbreak detection in public health surveillance systems. The MPINAR(1) model is proposed as a computationally tractable alternative to the general multivariate integer-valued autoregressive (MINAR(1)) model. While the MINAR(1) framework allows for correlated innovations, it introduces substantial estimation challenges and requires strong distributional assumptions that may not hold in practice. To address these limitations, the MPINAR(1) model simplifies the innovation structure by assuming that the innovation process consists of independent Poisson-distributed components. This assumption retains the discrete nature of the data while reducing computational complexity, allowing for efficient implementation using conditional maximum likelihood estimation. A simulation study is conducted to evaluate the performance of the MPINAR(1) model in detecting simulated outbreaks within trivariate count time series. The model is assessed against independent univariate INAR(1) models using metrics such as average run length (ARL), detection rate, and false alarm rate (FAR). Results show that the MPINAR(1) model outperforms the univariate alternatives, particularly in scenarios involving moderate to large outbreak sizes. The model is further applied to syndromic surveillance data comprising daily counts of fever, cough, and dyspnea among hospitalised COVID-19 patients. Covariate adjustments for dayof-week and seasonal effects are incorporated into the innovation process. The MPINAR(1) model demonstrates superior fit compared to univariate models, producing wider and more reliable prediction intervals and detecting additional potential outbreak events. Residual analyses confirm that the MPINAR(1) model provides a closer approximation to white noise and better captures temporal and cross-sectional dependencies. Overall, the MPINAR(1) model provides a theoretically sound and computationally efficient
framework for multivariate count time series modelling in surveillance settings. Its improved detection capabilities and robustness to overdispersion make it a valuable tool for enhancing early warning systems in public health. Future extensions could include more flexible innovation structures and refined alarm decision rules.