Mathematical Modeling of Infectious Diseases

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Description
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

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.
Date Created
2023
Agent

Four-Dimensional Geometry Visualization in Augmented Reality.pdf

Description
This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well

This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.
Date Created
2023-05
Agent

Four-Dimensional Geometry Visualization in Augmented Reality

Description

This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well

This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.

Date Created
2023-05
Agent

Higher-Order Network Analysis of Fine Particulate Matter (PM 2.5) Transport in China at City Level

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Description

Specification of PM2.5 transmission characteristics is important for pollution control and policymaking. We apply higher-order organization of complex networks to identify major potential PM2.5 contributors and PM2.5 transport pathways of a network of 189 cities in China. The network we

Specification of PM2.5 transmission characteristics is important for pollution control and policymaking. We apply higher-order organization of complex networks to identify major potential PM2.5 contributors and PM2.5 transport pathways of a network of 189 cities in China. The network we create in this paper consists of major cities in China and contains information on meteorological conditions of wind speed and wind direction, data on geographic distance, mountains, and PM2.5 concentrations. We aim to reveal PM2.5 mobility between cities in China. Two major conclusions are revealed through motif analysis of complex networks. First, major potential PM2.5 pollution contributors are identified for each cluster by one motif, which reflects movements from source to target. Second, transport pathways of PM2.5 are revealed by another motif, which reflects transmission routes. To our knowledge, this is the first work to apply higher-order network analysis to study PM2.5 transport.

Date Created
2017-10-16
Agent

Prediction and Control of Brucellosis Transmission of Dairy Cattle in Zhejiang Province, China

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Description

Brucellosis is a bacterial disease caused by brucella; mainly spread by direct contact transmission through the brucella carriers, or indirect contact transmission by the environment containing large quantities of bacteria discharged by the infected individuals. At the beginning of 21st

Brucellosis is a bacterial disease caused by brucella; mainly spread by direct contact transmission through the brucella carriers, or indirect contact transmission by the environment containing large quantities of bacteria discharged by the infected individuals. At the beginning of 21st century, the epidemic among dairy cows in Zhejiang province, began to come back and has become a localized prevalent epidemic. Combining the pathology of brucellosis, the reported positive data characteristics, and the feeding method in Zhejiang province, this paper establishes an SEIV dynamic model to excavate the internal transmission dynamics, fit the real disease situation, predict brucellosis tendency and assess control measures in dairy cows. By careful analysis, we give some quantitative results as follows. (1) The external input of dairy cows from northern areas may lead to high fluctuation of the number of the infectious cows in Zhejiang province that can reach several hundreds. In this case, the disease cannot be controlled and the infection situation cannot easily be predicted. Thus, this paper encourages cows farms to insist on self-supplying production of the dairy cows. (2) The effect of transmission rate of brucella in environment to dairy cattle on brucellosis spreading is greater than transmission rate of the infectious dairy cattle to susceptible cattle. The prevalence of the epidemic is mainly aroused by environment transmission. (3) Under certain circumstances, the epidemic will become a periodic phenomenon. (4) For Zhejiang province, besides measures that have already been adopted, sterilization times of the infected regions is suggested as twice a week, and should be combined with management of the birth rate of dairy cows to control brucellosis spread.

Date Created
2014-11-11
Agent