In response to a significant tuberculosis outbreak in Wyandotte and Johnson Counties, Kansas, this study presents a compartmental model of ordinary differential equations to evaluate the impact of standard antibiotic treatment. The model incorporates latent, active, and treated disease states. Parameter values were informed by epidemiological data and uncertain parameter value ranges were explored systematically through uncertainty analysis using constrained Latin hypercube sampling. Cumulative infections and deaths, and the basic reproduction number, were computed over a five-year simulation period. Sensitivity analyses using partial rank correlation coefficients identified symptomatic treatment rate and transmission rate as primary drivers of cumulative infections and deaths. Model results indicate that treatment significantly reduces both infections and mortality, but that relying solely on treatment has high associated costs underscoring the importance of integrating transmission mitigation measures alongside treatment. This modeling framework offers valuable insight for public health policy, especially in managing resource allocation during tuberculosis outbreaks.
Ischemic hepatitis (IH) results from shock-related conditions that impair oxygenated blood flow to the liver, causing hepatocyte death. Diagnosis relies largely on clinical history due to the absence of specific diagnostic tests and limited ability to predict outcomes. This study applies machine learning methods to real-world IH patient data to improve outcome prediction. Biomedical indicators analyzed include creatinine, international normalized ratio (INR), aspartate aminotransferase (AST), alanine transaminase (ALT), and bilirubin. Data were collected from multiple U.S. centers through the Acute Liver Failure Study Group (ALFSG), a multicenter network focused on this rare condition. We implemented logistic regression, regression tree methods (including random forests and Bayesian Additive Regression Trees), and neural networks. To enhance model performance, we applied Synthetic Minority Oversampling Technique (SMOTE), along with optimization and feature selection techniques. Results show that INR and bilirubin are consistently selected as key predictors across all models, which demonstrated comparable predictive performance.
Phenotypically plastic organisms are capable of adjusting their phenotypes in a variable environment. Padilla and Adolph (1996) modeled this process and included a time lag between detection of an environmental change and the responding change in phenotype. We extended the Padilla and Adolph model from two to three discrete environments and phenotypes and analyzed the model computationally. Our results were consistent with their findings: the fitness advantage of phenotypic plasticity is higher when (1) the lag time is shorter, (2) the probability of environmental change is lower, and (3) the fitness disadvantage of mismatched phenotypes and environments is more severe. Additionally, we observed that there is a critical lag time beyond which it is no longer advantageous to be phenotypically plastic, compared to being phenotypically fixed (unchanging), with the exception of special symmetric cases. Thus, lag time can be a critical determinant of whether phenotypic plasticity is favored.
Deforestation, driven by industrial agriculture and cattle farming, has significantly impacted communities and ecosystems across the globe. In this paper, we develop a discrete-time Markov model to evaluate the effectiveness of market-based interventions, such as payments for ecosystem services (PES) and taxes, in addressing forest loss within the context of large-scale agriculture. Specifically, we focus on how commodity price variability influences deforestation decisions. To model these price fluctuations, we represent agricultural prices as geometric Brownian motion (GBM). By linking commodity price dynamics to land use transitions, our model aims to provide insight into how financial mechanisms can slow or stop deforestation. We find that the structure of the implemented policies have a large effect even if the total dollar amount across different structures were to remain constant. Therefore, decision makers should carefully choose the structure of their policies depending on their objectives with regards to poverty alleviation, deforestation prevention, and reforestation incentives.
Antibody and cytokine kinetics describe the dynamic response to immune events such as infection and vaccination. These dynamics are not fully understood, and mathematical characterization may help explain variability across demographic groups and pulmonary symptoms post-acute infection. We fit time-dependent probability models to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data to obtain distributions of longitudinal antibody response and cytokine values. To assess differences between groups, an overlap metric is applied to the modeled response curves. Our antibody models suggest significant differences between male and female populations and demonstrate deficient antibody responses of less-healthy groups such as smokers. Our cytokine models suggest that those with pulmonary symptoms post-acute infection have elevated responses over time. Further, we find that the cytokine response increases and then decays more rapidly than the antibody response. These results are consistent with clinical observations.
In this paper, we introduce a novel framework using inhomogeneous Branching Random Walks (BRWs) to model growth processes, specifically introducing genealogy-dependence in branching rates and displacement distributions to model phenomena like bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such long-time asymptotics are of independent mathematical interest and are crucial in understanding the effect of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined model then uses a weighted average of positions given by these separate models to study the shape of the growth patterns. Using computer simulations, we tune parameters from these models, which are based on genealogical and spatiotemporal factors, observe the resulting structures, and compare them with images of real bacterial colonies.
This study examines the effects of environmental changes on fish populations in Norwalk Harbor, focusing on winter flounder (Pseudopleuronectes americanus), cunner (Tautogolabrus adspersus), northern pipefish (Syngnathus fuscus), and naked goby (Gobiosoma bosci) as examples of species responding to climate-related shifts. We analyze how water temperature, salinity, and dissolved oxygen correlate with fish abundance. To assess statistically significant differences in catch per unit effort (CPUE) across harbor regions, we applied the Kruskal-Wallis test followed by Dunn's post-hoc test. Seasonal variations in CPUE were examined by comparing monthly catch data for each species. K-means clustering revealed distinct environmental zones within the harbor, while Principal Component Analysis (PCA) identified the key environmental drivers shaping spatial patterns of water quality and species distribution.
Agent-based models (ABMs) are computer simulation models for studying systems of autonomous agents. Modelers often use specialized software like NetLogo to develop ABMs, but this software poses barriers to researchers in other disciplines with no prior programming experience. To address this issue, we developed a web application that allows users to simulate our ABM via a web browser, eliminating the need for the user to download and use specialized software. While presented in the context of a specific ABM, our approach can be applied to other ABMs to enhance accessibility. The ABM presented here was developed in NetLogo3D. The model simulates pain-related neural activity in the central nucleus of the amygdala and generates an emergent measure of pain output. The web application enables users to modify parameters, run simulations, visualize output, and export data without interacting with the model's code or downloading software, broadening access to researchers and the public.
Early prediction of response to therapy or lack thereof can help physicians plan treatment more efficiently. Biomarkers based on circulating tumor DNA (ctDNA) are promising. However, biomarkers beyond direct comparison to baseline have not been thoroughly explored. We develop a model for ctDNA shedding under targeted therapy that incorporates pharmacokinetics. Using a simulated cohort of virtual patients with varied parameters, we define and analyze a biomarker based on ctDNA samples at baseline, 12 hours, and 24 hours after initiation of treatment. The biomarker identified patients who would achieve partial or complete response with high sensitivity and specificity and was able to match the performance of a neural network classifier. Our result highlights the potential of ctDNA as a biomarker and underlines the importance of early ctDNA data collection. ### Competing Interest Statement The authors have declared no competing interest.
Whether immune cells protect or harm the brain is an open question depending on context, and their role is implicated in multiple diseases such as Alzheimer's disease, dementia, and other neurological disorders. Microglia, a specific type of immune cell in the central nervous system, play a key role in homeostasis, and genes associated with an elevated risk of Alzheimer's disease correspond with deficiencies in their behavior. We created an agent-based model that incorporates inflammatory signaling, chemotaxis, and phagocytosis of damaged neurons and allows the exploration of crucial pathways in the maintenance of brain health. We specifically investigated pathways related to Alzheimer's risk variants of the gene TREM2, which results in impaired microglia phagocytosis and sensing.
With due thanks to the Intercollegiate Biomathematics Alliance for their unending support, Spora is offering once again another highly respected platform for collaborative research in mathematics, biology, and related fields. Spora's role in disseminating work especially accessible to students 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 as well as original research.
In this exposition paper, we describe some computational methodologies to solve numerically differential equations modeling the shallow lake ecosystem, with particular focus on the dynamics of the phosphorus. We describe in detail Python implementations of classical algorithms, like Runge-Kutta, and more modern approaches, including physics-informed neural networks.
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 lower threshold for eradication than smallpox: a lower threshold for herd immunity, and vaccines that are more effective at reducing infections and deaths. Thus, our model analysis leads us to conclude that the persistence of polio is due to the persistence of inadequate vaccination rates in the remaining polio-endemic countries.
This study examines the correlation between political leanings and COVID-19 mortality across the states of America affiliated with Republican and Democratic governance. Employing emergent self-organizing map (ESOM), cluster analysis, and the logistic classification, we group states based on COVID-19 properties, identify risk patterns, and assess risk levels. Factors considered include poverty rate, education rate, vaccination rate, and demographics. The Logistic Algorithm succinctly summarizes findings, integrating ESOM, cluster analysis, and logistic classification results. This multi-method approach aims to offer a concise, yet comprehensive understanding of the COVID-19 risk landscape in politically diverse states, shedding light on potential associations between political affiliations and pandemic outcomes.
