Spatial Infectious Disease Transmission Models: Variable Screening Methods and Logistic Formulation.

Infectious disease outbreaks have widespread consequences, affecting not only health, economies, and agriculture, but also global trade, social structures, and education (Rohr et al., 2019; Vurro et al., 2010; Anderson, 2002). Advanced mathematical models of infectious diseases, particularly individual-level models (ILMs), play a crucial role in understanding and predicting disease dynamics at a detailed scale, facilitating targeted interventions, and developing new public health strategies for treatment and prevention. However, fitting these models can be challenging when there are numerous covariates involved. It is useful to filter relevant covariates from a wider range of potential covariates to enhance the model accuracy and prediction, increase computational efficiency, prevent over-fitting, and improve model robustness and interpretability. This thesis aims to investigate and compare various variable screening methods for individual-level disease transmission models. The methods include least absolute shrinkage and selection operator (Lasso), forward and backward stepwise Akaike information criterion (AIC), variable random selection (boosting) methods, spike-and-slab (SS) priors, and two-stage screening methods. These are applied within the context of spatial ILMs with numerous potential susceptible covariates. The methods are investigated on a combination of simulated epidemic data and UK foot-and-mouth disease outbreak data (2001). Additionally, we introduce a novel framework for modelling the spatiotemporal dynamics of disease transmission: the conditional logistic individual-level model (CL-ILM). This approach significantly reduces the computational complexity associated with traditional spatiotemporal ILMs, making it compatible with standard software for logistic model fitting. The modelling process is divided into two stages. First, we use a maximum likelihood approach to estimate the spatial parameter by selecting an optimal value from a finite set of plausible candidates, resulting in a conditional logistic ILM. In the second stage, the model is fitted within a Bayesian framework, and its performance is evaluated using a posterior predictive approach (Gardner, 2010). Moreover, we apply variable selection methods to the newly developed CL-ILMs to enhance model performance, improve interpretability, and minimize the risk of overfitting, ultimately leading to more robust and effective models. The performance of these methods is assessed and compared using both simulated data and the 2001 UK foot-and-mouth disease outbreak data.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Discipline thesis:degree_discipline

Mathematics & Statistics

Grantor

Science

Year dc:date.issued

2025

Author dc:creator

• Akter, Tahmina

Advisor dc:contributor.advisor

• Deardon, Rob

Committee members dc:contributor.committeemember

• Braun, Willard John
• Shen, Hua
• Wang, Haixu
• Liu, Juxin

• Spatial modelling
• Posterior predictive distribution
• Conditional logistic ILM
• Logistic ILM
• Spike-and-slab prior
• Forward and backward stepwise AIC
• Two-stage Lasso
• Variable selection
• Individual-level model (ILM)
• Disease transmission dynamics
• Infectious disease

Statement dc:rights

• Unless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

en

DOI

https://dx.doi.org/10.11575/PRISM/48587

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/120997