Author ORCID Identifier

https://orcid.org/0009-0001-1354-9233

Date of Award

8-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Dr. Alexandra Smirnova

Abstract

A clear understanding of the actual infection rate is imperative for control and prevention of diseases. This knowledge is essential in formulating effective vaccination strategies and assessing the level of herd immunity required to contain the virus. In recent years, advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for the design of adequate public health policies. This dissertation presents a theoretical and numerical study of a novel optimization procedure aimed to achieve a stable estimation of incidence reporting rates and time-dependent effective reproduction numbers using real data on new incidence cases, daily new deaths, and vaccination percentages. The iteratively regularized optimization algorithm introduced here is versatile and applicable to a wide range of data fitting problems constrained by various biological models, particularly those that need to account for under-reporting of cases. To support this, general nonlinear observation operators in real Hilbert spaces are used in the proposed convergence analysis. The theoretical findings are demonstrated through numerical simulations using the susceptible unvaccinated (S), susceptible vaccinated (V ), infected unvaccinated (Is), infected vaccinated (Iv), recovered (R), and deceased (D) compartmental model and real data from the Delta variant of the COVID-19 pandemic in different states of the US. In the second part of this dissertation, a biological model with a flexible choice of control strategies for an emerging virus is considered. In the model, the disease transmission is mitigated using both non-medical control (like social distancing and other behavioral changes) and the control by treatment with antiviral medication.

DOI

https://doi.org/10.57709/37370383

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