Nonlinear Dynamics, Stochastic Methods, And Predictive Modelling For Infectious Disease: Application To Public Health And Epidemic Forecasting

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dc.contributor.advisorWu, Jianhong
dc.contributor.authorPrashad, Christopher Daniel
dc.date.accessioned2025-04-10T10:53:38Z
dc.date.available2025-04-10T10:53:38Z
dc.date.copyright2024-12-09
dc.date.issued2025-04-10
dc.date.updated2025-04-10T10:53:37Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractStatistical models must adapt to the evolving nature of many processes over time. This thesis introduces flexible models and statistical methods designed to infer data-generating processes that vary temporally. The primary objective is to develop frameworks for efficient estimation and prediction of both univariate and multivariate time series data. The models considered are general dynamic predictive models with parameters that change over time, featuring time-varying regression coefficients or variance components. These models are capable of accommodating time-dependent covariates and can handle situations where information is incomplete. Several novel enhancements to existing mathematical models are introduced, with a particular focus on online learning and real-time prediction. Efficient Bayesian inference methodology is developed for analyzing the posterior of covariance components of dynamic models sequentially with a closed-form estimation algorithm for real-time online processing. Additionally, an online change detection algorithm for structural breaks is developed, combining the benefits of Kalman filters with sequential Monte Carlo methods. A general and extensible compartmental model for the study of infectious disease data is proposed, with several innovative extensions to established probability models for the analysis of data. Next, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model by integrating innovative stochastic mean-reverting transmission processes to more accurately capture the variability observed in real-world epidemic data. Lastly, we provide a methodology that harnesses expansive data sources and feature engineering for analyzing and forecasting peak time and height of epidemic waves, crucial for the planning of public health strategies and interventions. The performance of these inference methodologies is assessed through simulation experiments and real data from clinical, social-demographic, and epidemic domains.
dc.identifier.urihttps://hdl.handle.net/10315/42842
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subject.keywordsDynamic regression models
dc.subject.keywordsBayesian sequential inference
dc.subject.keywordsStochastic simulation
dc.subject.keywordsParticle filter
dc.subject.keywordsOnline prediction
dc.subject.keywordsCovariance estimation
dc.subject.keywordsStructural change detection
dc.subject.keywordsDisease transmission processes
dc.subject.keywordsMean reversion
dc.subject.keywordsStochastic threshold
dc.subject.keywordsInfectious disease modelling
dc.subject.keywordsEpidemic wave peak forecasting
dc.subject.keywordsPredictive modelling
dc.subject.keywordsMathematical epidemiology
dc.subject.keywordsPublic health
dc.titleNonlinear Dynamics, Stochastic Methods, And Predictive Modelling For Infectious Disease: Application To Public Health And Epidemic Forecasting
dc.typeElectronic Thesis or Dissertation

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