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- SIR model (4)
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- Acoustic deterrence (1)
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- Adaptive network model (1)
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- Aggressive conflict (1)
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Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine
A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine
Spora: A Journal of Biomathematics
The smallpox and poliomyelitis (polio) viruses were, at a time, one of the largest threats to global public health killing millions until global eradication campaigns were put into effect. Vaccination led to the eradication of smallpox and the elimination of polio for most of the world. However, polio continues to persist at endemic levels in Pakistan and Afghanistan. We developed ODE models of smallpox and polio to explore differences in transmission dynamics and determine if the underlying biology has made poliomyelitis more difficult to eradicate. Our model analysis shows there are multiple factors which should allow polio to have a …
A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry
A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry
Spora: A Journal of Biomathematics
Rhinoceros populations in Africa are in peril largely due to the high value of their horns and the poaching that ensues. The strategy of legalizing the international trade of rhino horn is receiving increased support among both the people and government officials in Africa. Many in the international conservation community remain opposed to the idea. The legalization strategy is straightforward in theory: legalizing the trade of rhino horn will introduce a large quantity of horn to the market, the increased supply will lead to lower prices for rhino horn, and lower prices will reduce the overall poaching pressure these animals …
Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans
Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans
Spora: A Journal of Biomathematics
Compartmental modeling serves as a necessary framework in many fields, especially biomathematics and ecology. This article introduces readers to a user-friendly approach to constructing compartmental models and solving the resulting systems of differential equations to simulate real-world applications. The platform used is Berkeley Madonna, a software package that has an intuitive graphical interface which empowers users—even those with limited mathematical and programming backgrounds—to focus on modeling concepts rather than mathematical or programming intricacies. This makes Berkeley Madonna an ideal platform for students, educators, and researchers.
Modeling The Population Demographics & Viability Of Imperiled Guzmania Monostachia Populations, Helen Pennington, Pranay Lingareddy, Erin N. Bodine
Modeling The Population Demographics & Viability Of Imperiled Guzmania Monostachia Populations, Helen Pennington, Pranay Lingareddy, Erin N. Bodine
Spora: A Journal of Biomathematics
Guzmania monostachia is a large, long-lived bromeliad whose leaves grow in a rosette pattern and is native to the Americas, but endangered in Florida due to damage caused by the invasive weevil Metamasius callizona. Each G. monostachia rosette can reproduce sexually via flowers or asexually by producing clonal offshoot rosettes. We model the population dynamics and demographic structure of a G. monostachia population using a Lefkovitch matrix model where each state represents a demographic class of rosettes. Model analysis over a range of uncertain parameters show the conditions under which a G. monostachia population is viable in the absence …
Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson
Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson
Spora: A Journal of Biomathematics
Silver carp (Hypophthalmichthys molitrix) are planktivorous fish that were originally introduced to the United States for use in fish production ponds and have since escaped these enclosures and are invading the Mississippi River Basin. The silver carp invasion of the Illinois River has a myriad of negative effects on native ecosystems. In this paper, we introduce key dependencies that are likely important in the population dynamics of silver carp: length-dependent egg production and density-dependent growth. Using movement data between two adjacent pools of the Illinois River, we conduct numerical simulations to explore the theoretical effect of harvesting and …
A Statistical Analysis Of The Change In Age Distribution Of Spawning Hatchery Salmon, Rachel Macaulay, Emily Barrett, Grace Penunuri, Eli E. Goldwyn
A Statistical Analysis Of The Change In Age Distribution Of Spawning Hatchery Salmon, Rachel Macaulay, Emily Barrett, Grace Penunuri, Eli E. Goldwyn
Spora: A Journal of Biomathematics
Declines in salmon sizes have been reported primarily as a result of younger maturation rates. This change in age distribution poses serious threats to salmon-dependent peoples and ecological systems. We perform a statistical analysis to examine the change in age structure of spawning Alaskan chum salmon Oncorhynchus keta and Chinook salmon O. tshawytscha using 30 years of hatchery data. To highlight the impacts of this change, we investigate the average number of fry/smolt that each age of spawning chum/Chinook salmon produce. Our findings demonstrate an increase in younger hatchery salmon populations returning to spawn, and fewer amounts of fry produced …
A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie
A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie
Spora: A Journal of Biomathematics
The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito Aedes aegypti. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of A. aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for A. aegypti.
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, Flavius Guias
Spora: A Journal of Biomathematics
This paper presents a mathematically formalized approach which points out the relation between efficacy and effectiveness of vaccines. The first term denotes the relative degree of protection in clinical trials or under ideal conditions, while the latter is based on observed real-life data. We define the efficacy by a similar formula to the effectiveness, but the probabilities involved in the relative risk are conditional with respect to the exposure to the virus. If exposure and vaccination status are independent, the two quantities are equal. Otherwise, the observed value of the effectiveness is a biased one, as it could be seen …
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Spora: A Journal of Biomathematics
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values.
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Spora: A Journal of Biomathematics
Radiation therapy remains as one of the main cancer treatment modalities. Typical regimens for radiotherapy comprise a constant dose administered on weekdays, and no radiation on weekends. In this paper, we examine adaptive dosages of radiation treatment strategies for heterogeneous tumors using a dynamical system model that consist of radiation-resistant and parental populations with unique interactive properties, namely, PC3 and DU145 prostate cancer cell lines. We show that stronger doses of radiation given in longer time intervals, while keeping the overall dosage the same, are effective in PC3 cell lines, but not in DU145 cell lines. In addition, we tested …
An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, W. Zane Billings, Justin Clifton, Josh Hiller, Tommy Meek, Andrew Penland, Wesley Rogers, Gabriella Smokovich, Andrew Velasquez-Berroteran, Eleni Zamagias
An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, W. Zane Billings, Justin Clifton, Josh Hiller, Tommy Meek, Andrew Penland, Wesley Rogers, Gabriella Smokovich, Andrew Velasquez-Berroteran, Eleni Zamagias
Spora: A Journal of Biomathematics
In 1954, Armitage and Doll published one of the most influential papers in the history of mathematical epidemiology. However, when one examines the literature one finds that there are in fact at least three distinct mathematical models attributed to the 1954 paper. In this study, we examine this important paper and the mathematical derivation of their model. We find, very surprisingly, that no stochastic process can account for all the assumptions of the model and that many of the models in the literature use a consistent subset of the assumptions used in Armitage and Doll's paper.
Epidemic Conditions With Temporary Link Deactivation On A Network Sir Disease Model, Hannah Scanlon, John Gemmer
Epidemic Conditions With Temporary Link Deactivation On A Network Sir Disease Model, Hannah Scanlon, John Gemmer
Spora: A Journal of Biomathematics
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to avoid infection while also maintaining preexisting, interpersonal relationships. Specifically, we use a network model in which individuals probabilistically deactivate connections to infected individuals and later reconnect to the same individuals upon recovery. To analyze this network model, a mean field approximation consisting of a system of fourteen ordinary differential equations for the number of nodes and edges is developed. This system …
Empirical Fitting Of Periodically Repeating Environmental Data, Pavel Bělík, Andrew Hotchkiss, Brandon Perez, John Zobitz
Empirical Fitting Of Periodically Repeating Environmental Data, Pavel Bělík, Andrew Hotchkiss, Brandon Perez, John Zobitz
Spora: A Journal of Biomathematics
We extend and generalize an approach to conduct fitting models of periodically repeating data. Our method first detrends the data from a baseline function and then fits the data to a periodic (trigonometric, polynomial, or piecewise linear) function. The polynomial and piecewise linear functions are developed from assumptions of continuity and differentiability across each time period. We apply this approach to different datasets in the environmental sciences in addition to a synthetic dataset. Overall the polynomial and piecewise linear approaches developed here performed as good (or better) compared to the trigonometric approach when evaluated using statistical measures (R2 …
Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer
Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer
Spora: A Journal of Biomathematics
Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …
Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis
Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis
Spora: A Journal of Biomathematics
Though clinicians can now collect detailed information about a variety of tumor characteristics as a tumor evolves, it remains difficult to predict the efficacy of a given treatment prior to administration. Additionally, the process of data collection may be invasive and expensive. Thus, the creation of a framework for predicting patient response to treatment using only information collected prior to the start of treatment could be invaluable. In this study, we employ ordinary differential equation models for tumor growth and utilize synthetic data from a cellular automaton model for calibration. We investigate which parameters have the most influence upon treatment …
Kleptoparasitic Hawk-Dove Games, Isabella H. Evans-Riester, Chasity T. Kay, Karina L. Ortiz-Suarez, Jan Rychtář, Dewey Taylor
Kleptoparasitic Hawk-Dove Games, Isabella H. Evans-Riester, Chasity T. Kay, Karina L. Ortiz-Suarez, Jan Rychtář, Dewey Taylor
Spora: A Journal of Biomathematics
The Hawk-Dove game is a classical game-theoretical model of potentially aggressive animal conflicts. In this paper, we apply game theory to a population of foraging animals that may engage in stealing food from one another. We assume that the population is composed of two types of individuals, Hawks and Doves. Hawks try to escalate encounters into aggressive contests while Doves engage in non-aggressive displays between themselves or concede to aggressive Hawks. The fitness of each type depends upon various natural parameters, such as food density, the mean handling time of a food item, as well as the mean times of …
A Dynamic Energy Budget Model Of Ornate Box Turtle Shell Growth, Tyler Skorczewski, Brandon Andersen
A Dynamic Energy Budget Model Of Ornate Box Turtle Shell Growth, Tyler Skorczewski, Brandon Andersen
Spora: A Journal of Biomathematics
Many aspects of box turtle development may depend on size rather than age. Notable examples include sexual maturity and the development of the fully closing hinge in the shell that allows box turtles to completely hide in their shells. Thus, it is important to understand how turtles grow in order to have a complete understanding of turtle biology. Previous studies show that turtle shell growth behaves in a logistic manner. These studies use functional models that fit the data well but do little to explain mechanisms. In this work we use the ideas found in dynamic energy budget theory to …
Flattening The Curve: The Effects Of Intervention Strategies During Covid-19, Kelly A. Reagan, Rachel J. Pryor, Gonzalo M. Bearman, David M. Chan
Flattening The Curve: The Effects Of Intervention Strategies During Covid-19, Kelly A. Reagan, Rachel J. Pryor, Gonzalo M. Bearman, David M. Chan
Spora: A Journal of Biomathematics
COVID-19 has plagued countries worldwide due to its infectious nature. Social distancing and the use of personal protective equipment (PPE) are two main strategies employed to prevent its spread. A SIR model with a time-dependent transmission rate is implemented to examine the effect of social distancing and PPE use in hospitals. These strategies’ effect on the size and timing of the peak number of infectious individuals are examined as well as the total number of individuals infected by the epidemic. The effect on the epidemic of when social distancing is relaxed is also examined. Overall, social distancing was shown to …
Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz
Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz
Spora: A Journal of Biomathematics
One of many risks facing HIV+ individuals is the development of kidney dysfunction and end stage kidney disease (ESKD). A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to kidney disease and on reducing mortality due to kidney failure. Analytical and numerical predictions of long-term HIV+ ESKD prevalence show that therapy can lead to either extremely low levels of disease prevalence or increased prevalence, depending on drug efficacy levels and mechanisms of action. Maintenance of HIV+ ESKD prevalence below one individual is possible with sufficient efficacy (e.g., 99%) against the progression from …
Modeling The Effects Of Passive Immunity In Birds For The Disease Dynamics Of West Nile Virus, Noelle West, Vinodh K. Chellamuthu
Modeling The Effects Of Passive Immunity In Birds For The Disease Dynamics Of West Nile Virus, Noelle West, Vinodh K. Chellamuthu
Spora: A Journal of Biomathematics
West Nile Virus (WNV) is a mosquito-borne virus that circulates among birds but also affects humans. Migrating birds carry these viruses from one place to another each year. WNV has spread rapidly across the continental United States resulting in numerous human infections and deaths. Several studies suggest that larval mosquito control measures should be taken as early as possible in a season to control the mosquito population size. Also, adult mosquito control measures are necessary to prevent the transmission of WNV from mosquitoes to birds and humans. To better understand the effective strategy for controlling affected larvae mosquito population, we …
A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine
A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine
Spora: A Journal of Biomathematics
The large, long-lived, epiphytic bromeliad Tillandsia utriculata is currently listed as state-endangered in Florida due to significant population reduction from predation by an invasive weevil, Metamasius callizona. We have developed a novel demographic model of a population of T. utriculata in Myakka River State Park (MRSP) in Sarasota, Florida using a stage-structured matrix model. Analysis of the model revealed conditions for population viability over a variety of parameter scenarios. Model analysis showed that without weevil predation the minimum germination rate required for population viability is low (4–16%), and that given a viable population at structural equilibrium we would expect …
Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri
Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri
Spora: A Journal of Biomathematics
Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.
Combating Tuberculosis: Using Time-Dependent Sensitivity Analysis To Develop Strategies For Treatment And Prevention, Kendall B. Clark, Mayleen Cortez, Cristian Hernandez, Beth E. Thomas, Allison L. Lewis
Combating Tuberculosis: Using Time-Dependent Sensitivity Analysis To Develop Strategies For Treatment And Prevention, Kendall B. Clark, Mayleen Cortez, Cristian Hernandez, Beth E. Thomas, Allison L. Lewis
Spora: A Journal of Biomathematics
Although many organizations throughout the world have worked tirelessly to control tuberculosis (TB) epidemics, no country has yet been able to eradicate the disease completely. We present two compartmental models representing the spread of a TB epidemic through a population. The first is a general TB model; the second is an adaptation for regions in which HIV is prevalent, accounting for the effects of TB/HIV co-infection. Using active subspaces, we conduct time-dependent sensitivity analysis on both models to explore the significance of certain parameters with respect to the spread of TB. We use the results of this sensitivity analysis to …
Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell
Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell
Spora: A Journal of Biomathematics
Studies done on interactions between spores and macrophages done in vitro show inconsistent results based on experimental protocol and inhibit meaningful extrapolation to in vivo. In this study, we perform a sensitivity analysis of a model representing in vitro studies of interactions between anthrax spores and macrophages to help address the effects of these inconsistencies. We perform both local and global analyses using Latin hypercube sampling and partial rank correlation coefficients. Our analysis indicates the amount of intracellular bacteria over time is most sensitive to the killing of intracellular bacteria by the macrophages and replication of the bacteria inside …
Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, Ami Radunskaya, Ruby Kim, Timothy Woods Ii
Mathematical Modeling Of Tumor Immune Interactions: A Closer Look At The Role Of A Pd-L1 Inhibitor In Cancer Immunotherapy, Ami Radunskaya, Ruby Kim, Timothy Woods Ii
Spora: A Journal of Biomathematics
Monoclonal antibodies have shown promising results as a form of cancer immunotherapy used either alone or in combination with another treatment. We model a monoclonal antibody in combination with a dendritic cell (DC) vaccine in order to study treatment optimization. Certain proteins on tumor cells allow the tumor cells to bind to specific receptors on immune cells, rendering the immune cells ineffective. Experiments using mouse models show that a combination of antibodies to these proteins with tumor suppressing drugs improves the effectiveness of cancer vaccines. We create independent models of each of the two treatments in combination with DC therapy, …
Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz
Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz
Spora: A Journal of Biomathematics
We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …
Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla
Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla
Spora: A Journal of Biomathematics
The circadian clock, responsible for coordinating organism function with daily and seasonal changes in the day-night cycle, is controlled by a complex protein network that constitutes a robust biochemical oscillator. Deterministic ordinary differential equation models have been used extensively to model the behavior of these central clocks. However, due to the small number of proteins involved in the circadian oscillations, mathematical models that track stochastic variations in the numbers of clock proteins may reveal more complex and biologically relevant behaviors. In this paper, we compare the response of a robust yet detailed deterministic model for the mammalian circadian clock with …
Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly
Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly
Spora: A Journal of Biomathematics
As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitation-contraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical …
Age-Structured And Vaccination Models Of Devil Facial Tumor Disease, Christopher D. Bruno, Timothy Comar, Megan O. Powell, Adjo Tameklo
Age-Structured And Vaccination Models Of Devil Facial Tumor Disease, Christopher D. Bruno, Timothy Comar, Megan O. Powell, Adjo Tameklo
Spora: A Journal of Biomathematics
Tasmanian devil populations have been devastated by devil facial tumor disease (DFTD) since its first appearance in 1996. The average lifespan of a devil has decreased from six years to three years. We present an age-structured model to represent how the disease has affected the age and breeding structures of the population. We show that with the recent increase in the breeding of juvenile devils, the overall devil population will increase but not nearly to pre-DFTD levels. The basic reproductive number may be increased with the influx of young breeding devils. In addition, our model shows that the release of …