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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson
A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson
Mathematics and Applied Mathematics Publications
We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …
A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly
A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly
Mathematics and Applied Mathematics Publications
Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …
A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal
A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal
Mathematics and Applied Mathematics Publications
In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between …
Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson
Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson
Mathematics and Applied Mathematics Publications
In this study, we use a discrete, two-patch population model of an Allee species to examine different methods in managing invasions. We first analytically examine the model to show the presence of the strong Allee effect, and then we numerically explore the model to test the effectiveness of different management strategies. As expected invasion is facilitated by lower Allee thresholds, greater carrying capacities and greater proportions of dispersers. These effects are interacting, however, and moderated by population growth rate. Using the gypsy moth as an example species, we demonstrate that the effectiveness of different invasion management strategies is context-dependent, combining …