Predicting Tumor Response to Radiotherapy Based on Estimation of Non-Treatment Parameters

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 efficacy by comparing parameter distributions associated with treatment outcomes. Additionally, we develop a framework for estimating the probability of observing complete tumor remission following a simulated radiotherapy regimen based only on a patient’s non-treatment parameters, so that treatment efficacy could be predicted prior to administration.

Fostering Research and Education in Mathematical Biology

As it is releasing the seventh volume, Spora has established itself to be a highly respected journal for student-driven research in mathematics, biology, and related fields. Spora's role in disseminating work that was conducted by at least one student author makes it a unique platform to expand the body of knowledge in mathematical biology. Spora welcomes submissions related to Ph.D. dissertations, master's theses, and undergraduate research projects.

A Study of COVID-19 Mortality Under Varying Patient Frailty

For this study, we modeled the spread and mortality of COVID-19 throughout the city of Chicago. By incorporating group frailty into a classic SEIR infectious disease model, we were able to differentiate the population of Chicago by their response to COVID-19. Three age groups with different COVID-19-induced death rates were examined, and the model sought to showcase the multiplicative deviation of each age group death rate from the average disease-induced death rate. This adjustment for different death rates among age groups accounted for heterogeneity within the population, and sought to introduce a more accurate manner for modeling the spread of infectious diseases.

A Dynamic Energy Budget Model of Ornate Box Turtle Shell Growth

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 build a model of box turtle shell growth. We show this model fits the data as well as previous models for ornate box turtles Terrapene ornata ornata, but also offers explanations for observed phenomena, such as maximum sizes and the appearance of biphasic growth.

Kleptoparasitic Hawk-Dove Games

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 conflicts over the food. We find the Evolutionarily Stable States (ESSs) for all parameter combinations and show that there are two possible ESSs, pure Hawks, or a mixed population of Hawks and Doves. We demonstrate that for any set of parameter values there is exactly one ESS.

Flattening the Curve: The effects of intervention strategies during COVID-19

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 cause the largest impact in the number of infections. Studying this interaction between social distancing and PPE use is novel and timely. We show that decisions made at the state level on implementing social distancing and acquiring adequate PPE have dramatic impact on the health of its citizens.

A Demographic Model of an Endangered Florida Native Bromeliad (Tillandsia utriculata)

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 to find <1% of the population in flower or post-flowering each year and, at most, about 10% of rosettes with longest leaf length (LLL) > 15 cm in flower or post-flowering each year. Additionally, the model presented here provides a basis for further analyses which explore specific conservation strategies.

A Mathematical Model for the Effect of Social Distancing on the Spread of COVID-19

Social distancing is an effective method of impeding the spread of a novel disease such as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), but is dependent on public involvement and is susceptible to failure when sectors of the population fail to participate. A standard SIR model is largely incapable of modeling differences in a population due to the broad generalizations it makes such as uniform mixing and homogeneity of hosts, which results in lost detail and accuracy when modeling heterogeneous populations. By further compartmentalizing an SIR model, via the separation of people within susceptible and infected groups, we can more accurately model epidemic dynamics and predict the eventual outcome, highlighting the importance of societal participation in social distancing measures during novel outbreaks.

Period Estimation and Noise in a Neutrally Stable Stochastic Oscillator

The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems.

Modeling the Effects of Passive Immunity in Birds for the Disease Dynamics of West Nile Virus

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 have developed a mathematical model using a system of first order differential equations to investigate the transmission dynamics of WNV in a mosquito-bird-human community. We also incorporated vertical transmission in mosquitoes and passive immunity in birds to more accurately simulate the spread of the disease.