CBBS Subgroup Contributed Talks

Xueying Wang

Washington State Univeristy

"Impact of Varying Networks on Disease Invasion"

We consider the spread of an infectious disease in a heterogeneous environment, modelled as a network of patches. We focus on the invasibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, $mathcal{R}_0$, and study how changes in the network structure affect the value of $mathcal{R}_0$. We provide a detailed analysis for two model networks, a star and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in $mathcal{R}_0$. We develop both combinatorial and matrix analytic techniques, and illustrate our theoretical results by simulations with the exact $mathcal{R}_0$.

Shaza Alsibaai

Department of Mathematics & Statistics, McGill University, Montréal, Canada.

"The Necessity of Including a Sub-model for Iron Metabolism in Mathematical Modelling of Erythropoiesis"

Erythropoiesis is a tightly regulated process beginning from hematopoietic stem cells (HSCs) and ending with mature red blood cells (RBCs). Hemoglobin within RBCs is responsible for transporting oxygen to body tissues. During erythropoiesis, about 20 to 25 mg of iron are used each day for hemoglobin synthesis, and most of this comes from recycling senescent RBCs. Many mathematical models of erythropoiesis in the literature neglect iron metabolism during erythropoiesis. However, such models are not useful in scenarios where there is iron overload or iron deficiency. At the same time, to understand the underlying control mechanisms, we seek to minimize the number of variables in the model, to circumvent issues with parameter identifiability that arise in ODE many-compartment models. In this talk, I will discuss a mathematical model we propose to capture the main physiological features of erythropoiesis. The model consists of five coupled delay differential equations, three of which track the iron during erythropoiesis including the hemoglobin iron within RBCs, and the other two equations model the dynamics of the major regulating hormones. I will present the derivation of the model, the positivity property of the model's solutions and the stability of its homeostatic steady state, and its numerical implementation.

Gess Iraji

Brandeis University

"Mathematical Modeling of Clogging in Microfluidic Structures from Simple to Complex Geometries"

We develop a mean-field model to study clogging in microfluidic devices and microvascular networks. Clogging in microfluidic cell sorters, which sort cells based on deformability, leads to disruptions in their performance, lower predictability and reliability, and a shorter lifetime in some cases. Our mean-field approach predicts the time of failure of single-column devices with a constant pressure gradient, constant flow rate, or independent channels. In addition, it provides insight into the clogging time and behavior of multiple-column devices and more complex porous structures, such as microvascular networks. To confirm our results, we use a time-driven stochastic simulation, numerically solve systems of differential equations, and use tools from probability theory and reliability engineering. In the case of capillary beds, we consider how the graph Laplacian spectrum provides some insight into the progress of clogging in the network.