Author: | Wei, Haozhen |
Title: | The reinfection and time to extinction of SARS-COV-2 in the SIR (susceptible-infected-removed) model with realistic distributions |
Advisors: | He, Daihai (AMA) |
Degree: | Ph.D. |
Year: | 2024 |
Subject: | Communicable diseases -- Mathematical models Epidemiology -- Mathematical models COVID-19 (Disease) -- Epidemiology Hong Kong Polytechnic University -- Dissertations |
Department: | Department of Applied Mathematics |
Pages: | 1 volume (unpaged) : color illustrations |
Language: | English |
Abstract: | For centuries, epidemics have posed significant threats to human health, and the emergence of the COVID-19 pandemic in 2019 heightened global awareness of the devastating impacts of infectious diseases. To address this challenge, extensive research has been conducted using mathematical models to elucidate the dynamics of epidemic spread, including infection rates, fatalities, and epidemic duration. This body of work has led to the advancement of epidemic modeling, highlighting the development and intricacies of the susceptible–infectious–recovered (SIR) model, the concept of the basic reproduction number, and stability analysis within this context. As our understanding of epidemics deepens, it becomes apparent that while foundational, traditional SIR models are limited by simplified assumptions. For instance, they do not fully accommodate the complexities observed in real-world epidemic scenarios, such as variable infectious periods and partial immunity post-recovery. Consequently, the field has seen the evolution of models such as SEIR (susceptible–exposed–infected–removed), which incorporates the latency period of the virus, and SIS (susceptible–infected–susceptible), which considers the possibility of reinfection after recovery. Selecting an appropriate model hinges on the research objectives, the characteristics of the disease under investigation, and data availability. A critical aspect of this selection process is considering infection phase distributions, which significantly influence the modeling and study of epidemics. The aim of the research reported herein is to develop an SIR model that incorporates multiple infection stages or a realistically distributed infection phase, thereby representing infectious disease dynamics in a more nuanced way than do traditional models. Incorporating realistic distributions—such as gamma or general probability distributions—enhances our comprehension of transmission dynamics and the efficacy of control measures. Previous findings indicate that using more-realistic distributions can affect key epidemic metrics, including peak infection numbers, epidemic timescales, and peak timing estimates. Furthermore, integrating a duration-dependent transmission rate—which decreases over the course of an infection—refines the estimation of the time-varying reproduction number, with significant implications for disease management and prevention. This thesis is structured as follows. In Chapter 1, the background and importance of the research are introduced. Chapter two and chapter three are the theoretical part. In Chapter 2, the historical development of epidemic models is outlined, focusing on the classical and simplest SIR model, then its properties are studied by incorporating the recruit rate into the model, calculating the basic reproduction number using the next-generation matrix method, and analyzing the stability of the SIR model. In Chapter 3, the limitations of the basic SIR model are discussed, particularly its assumption of an exponentially distributed infection period. In response to those limitations, some more-realistic distributions are introduced, i.e., the gamma distribution, the Erlang distribution, the Weibull distribution, the negative binomial distribution, and the log-normal distribution. Next, focus shifts to an enhanced SIR model using the Erlang distribution, constructing the SInR model (dividing the infectious period into the n stages), calculating the basic reproduction number, and conducting a stability analysis. The topic of extinction in epidemic diseases is then studied, and the results show that the transmission rate can affect the expected time of extinction. Next, the utility of mathematical modeling and theoretical analysis in understanding and predicting the disease extinction process is emphasized. The focus is on the SInR model and how the infection cycle parameter n affects the extinction timing, with a formula proposed for maintaining a constant extinction time irrespective of the value of n. Chapters 4 and 5 are about the application of COVID-19 research. In Chapter 4, the role of reinfections in Brazil’s second epidemic wave in 2021 is investigated, with the conclusion that reinfections played a minor role during the Delta-variant outbreak. The changes in Case Fatality Rate could be one of the factors under the observed multiple death waves due to COVID-19, thus we study the CFR in chapter 5, a meta-analysis of global COVID-19 mortality. Finally, conclusions and future directions are presented in Chapter 6. |
Rights: | All rights reserved |
Access: | open access |
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