Variance functions and Taylor's law of fluctuation scaling The variance function of a family of nonnegative random variables (rvs) gives the variance of each rv as a function of its mean, assuming each rv has finite mean and finite variance. Variance functions were invented to assist statistical analyses of agricultural experiments. They have since (under …
Coinfection dynamics of heroin transmission and HIV infection in a single population We propose a coinfection model of heroin abuse and HIV infection, to describe the joint spread through a single population. The unique disease-free equilibrium always exists and it is stable only if the basic reproduction numbers of heroin abuse and HIV infection are …
The SCMB Annual Symposium is a forum to exchange ideas between the broader mathematics and biosystems communities. There will be plenary talks from mathematicians and biologists, organized in complementary pairs, as well as a a public lecture. These will be offered at a colloquium level of detail with an emphasis on engaging the full range of mathematical and biological researchers. A poster …
Modelling interactions between disease dynamics and human social dynamics The interplay between disease dynamics and vaccinating behaviour driven by social processes has been receiving increasing attention from mathematical modellers, due to vaccine refusal and other behavioural phenomena. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases, on account of …
Trendy: Segmented regression analysis of gene expression dynamics High-throughput expression profiling experiments with ordered conditions (e.g. time-course or spatial-course) are becoming more common for studying detailed differentiation processes or spatial patterns. Identifying dynamic changes at both the individual gene and whole transcriptome level can provide important insights about genes, pathways, and critical time points.
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 …
