Mathematical Modeling of Infectious Diseases

The current coronavirus disease 2019 (COVID-19) pandemic has highlighted the crucial role of mathematical models in predicting, assessing, and controlling potential outbreaks. Numerous modeling studies using statistics or differential equations have been proposed to analyze the COVID-19 dynamics, with network analysis and cluster analysis also being adapted to understand disease transmission from multiple perspectives. This dissertation explores the use of network science and mathematical models to improve the understanding of infectious diseases. Chapter 1 provides an introduction to infectious disease modeling, its history, importance, and challenges. It also introduces network science as a powerful tool for understanding the complex interactions between individuals that can facilitate disease spread. Chapter 2 develops a statistical model that describes HIV infection and disease progression in a men who have sex with men cohort in Japan receiving a Pre-Exposure Prophylaxis (PrEP) program. The cost-effectiveness of the PrEP programwas evaluated by comparing the incremental cost-effectiveness ratio over a 30-year period against the willingness to pay threshold. Chapter 3 presents an ordinary differential equations model to describe disease transmission and the effects of vaccination and mobility restrictions. Chapter 4 extends the ODE model to include spatial heterogeneity and presents partial differential equations models. These models describe the combined effects of local transmission, transboundary transmission, and human intervention on COVID-19 dynamics. Finally, Chapter 5 concludes the dissertation by emphasizing the importance of developing relevant disease models to understand and predict the spread of infectious diseases by combining network science and mathematical tools.