College of Graduate Studies: Theses & Dissertations
Term of Award
Spring 2026
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Divine Tito F. Wanduku
Committee Member 1
Ionut Emil Iacob
Committee Member 2
Ahmed Al-Taweel
Committee Member 3
Chidozie William Chukwu
Abstract
Misspecification of stochastic error structure in nonlinear epidemic models can lead to biased inference and misleading model selection. This study develops and compares likelihood-based estimation methods for nonlinear compartmental ordinary differential equation epidemic models, with a primary focus on the Susceptible-Infected-Susceptible framework, under four alternative noise specifications: (i) independent white noise (nonlinear least squares), (ii) AR(1), (iii) AR(1)–MA(1), and (iv) RW–MA(1) processes. A unified computational maximum likelihood framework is constructed for the joint estimation of epidemiological and dependence parameters, using iterative optimization methods designed to ensure numerical stability in nonlinear settings. The proposed methods are applied to simulated short-horizon epidemic time series data. Model performance and goodness-of-fit are assessed using Akaike Information Criterion (AIC), mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE). Results demonstrate that, over short time horizons, the deterministic nonlinear dynamics dominate the observed behavior, while more complex correlated error structures provide limited improvement in fit and may introduce unnecessary variability in parameter estimates. These findings underscore the importance of carefully validating serial dependence assumptions in nonlinear time series epidemic models and provide a systematic framework for integrating dynamic transmission structures with stochastic dependence in likelihood-based inference.
Recommended Citation
Olofin, Daniel O., "Computational Maximum Likelihood Estimation for Nonlinear Compartmental ODE Epidemic Models with Correlated Time Series Errors" (2026). College of Graduate Studies: Theses & Dissertations. 3115.
https://digitalcommons.georgiasouthern.edu/etd/3115
Research Data and Supplementary Material
Yes
