Mathematical Biology

Network Analyses of Murine Glomeruli Kidneys filter blood through capillary bundles called glomeruli. Improved understanding of glomerular topological and spatial structure may inform our understanding of its development and function. We devised a new imaging approach to 12 murine glomeruli, using automated microtome tape to collect .5-micron serial sections and scanning electron microscopy to image …

Basic reproduction numbers for a class of reaction-diffusion epidemic models We study the basic reproduction numbers for a class of reaction-diffusion epidemic models that are developed from autonomous ODE systems. A general numerical framework is applied to compute such basic reproduction numbers; meanwhile, the numerical formulation provides useful insight into their characterizations. Using matrix analysis, …

A Network Immuno-epidemiological Model of HIV and Opioid Epidemics Severe Substance Abuse Disorder (commonly known as Addiction), and HIV individually claim many lives all over the world every year. But the spread of HIV is often due to intravenous drug usage, and drug usage by HIV positive people often lower their immunity and effectiveness of …

A dynamic model to assess human papillomavirus vaccination strategies in a heterosexual population combined with men who have sex with men Vaccination is effective in preventing human papillomavirus (HPV) infection. Who should be vaccinated and what's the best vaccine distribution strategy need more investigation. In this paper, we use a dynamic model to assess HPV …

Mathematics and the Life Sciences The close connection between mathematics and the physical sciences during the past century has been of great benefit to both. New mathematics has been inspired by problems in physics, while physics benefited from the theoretical power of mathematics in fundamental ways. The relationship between mathematics and the life sciences has …

How does interspecific host competition alter the amplification and dilution of disease? For pathogens that infect multiple host species, the loss or addition of one host species in a community can affect levels of disease in other host species. Using a 2-host, 1-pathogen epidemiological model, I explore how competition for resources between host species alters …