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This study introduces a stochastic model of COVID-19 transmission tailored to the Colorado School of Mines campus and evaluates surveillance testing strategies within a university context. Enhancing the conventional SEIR framework with stochastic transitions, our model accounts for the unique characteristics of disease spread in a residential college, including specific states for testing, quarantine, and isolation. Employing an approximate Bayesian computation (ABC) method for parameter estimation, we navigate the complexities inherent in stochastic models, enabling an accurate fit of the model with the campus case data. We then studied our model under the estimated parameters to evaluate the efficacy of different testing policies that could be implemented on a university campus. This framework not only advances understanding of COVID-19 dynamics on the Mines campus but serves as a blueprint for comparable settings, providing insights for informed strategies against infectious diseases., Comment: Under review

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain., Comment: Repository: https://github.com/d-montgomery/clotFoam

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury, which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODE) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical ADP hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool., Comment: 35 pages, 14 figures

We investigate 3-dimensional flagellar swimming in a fluid with a sparse network of stationary obstacles or fibers. The Brinkman equation is used to model the average fluid flow where a flow-dependent term, including a resistance parameter that is inversely proportional to the permeability, models the resistive effects of the fibers on the fluid. To solve for the local linear and angular velocities that are coupled to the flagellar motion, we extend the method of regularized Brinkmanlets to incorporate a Kirchhoff rod, discretized as point forces and torques along a centerline. Representing a flagellum as a Kirchhoff rod, we investigate emergent waveforms for different preferred strain and twist functions. Since the Kirchhoff rod formulation allows for out-of-plane motion, in addition to studying a preferred planar sine wave configuration, we also study the case with a preferred helical configuration. Our numerical method is validated by comparing results to asymptotic swimming speeds derived for an infinite-length cylinder propagating planar or helical waves. Similar to the asymptotic analysis for both planar and helical bending, we observe that with small amplitude bending, swimming speed is always enhanced relative to the case with no fibers in the fluid (Stokes) as the resistance parameter is increased....

Many microorganisms swim in a highly heterogeneous environment with obstacles such as fibers or polymers. To better understand how this environment affects microorganism swimming, we study propulsion of a cylinder or filament in a fluid with a sparse, stationary network of obstructions modeled by the Brinkman equation. The mathematical analysis of swimming speeds is investigated by studying an infinite-length cylinder propagating lateral or spiral displacement waves. For fixed bending kinematics, we find that swimming speeds are enhanced due to the added resistance from the fibers. In addition, we examine the work and the torque exerted on the cylinder in relation to the resistance. The solutions for the torque, swimming speed, and work of an infinite-length cylinder in a Stokesian fluid are recovered as the resistance is reduced to zero. Finally, we compare the asymptotic solutions with the numerical results obtained from the Method of Regularized Brinkmanlets. The swimming speed of a finite-length filament decreases as its length decreases and planar bending induces an angular velocity that increases linearly with added resistance. The comparisons between the asymptotic analysis and computation give insight on the effect of the length of the filament, the permeability, and the thickness of the cylinder in terms of the overall performance of planar and helical swimmers, Comment: 33 pages, 21 figures