Contributed Talks Session 2


Paul Cazeaux, University of Kansas
Agnieszka Miedlar, University of Kansas


Sunday, October 3, 2021 at 11:00 am – 12:20 pm (CST)


Md Rafiul Islam
Iowa State University
11:00 am

Evaluation of the United States COVID-19 Vaccine Allocation Strategy

To evaluate the U.S. Centers for Disease Control and Prevention‚ Äôs (CDC) COVID-19 vaccine prioritization strategy we developed a mathematical model that takes into account various characteristics influencing the spread and severity of the disease (age, profession, comorbidities, and living conditions). We determined the globally optimal vaccine allocation strategy for four outcomes (mortality, cases, infections, and years of life lost), and verified that the CDC strategy performed well in all outcomes although never optimally. Variation in poorly understood disease parameters did not affect the optimal allocation choice, while differences in vaccine function did. The developed global optimization approach can be used for future mass vaccination campaigns, and can be adapted for use by other countries seeking to evaluate and optimize their current prioritization strategies.

Daniel Jonas
Colorado State University
11:20 am

A Mathematical Model of Immunity and Tolerance of Disease

When an organism is challenged with a novel pathogen a cascade of events unfolds. The innate immune system rapidly mounts a preliminary nonspecific defense, while the acquired immune system slowly develops microbe-killing specialists. These responses cause inflammation and collateral damage, which the anti-inflammatory mediators seek to temper. This interplay of counterbalances is credited for maintaining health, but it may produce unexpected results such as disease tolerance. This outcome is characterized by the persistence of pathogen with minimum deleterious effects to the host, who is often capable of spreading it to others. Tolerance is poorly understood, indicating a need for theoretical study. Accordingly, we present a novel differential equation model of infection and immunity derived from bulk fundamental interactions and demonstrate that it can produce clinically relevant health and death scenarios. Model simulation and numerical analysis show that these states are determined by pathogen virulence and the strength of the innate response to trauma. By exploring various regions of parameter space, we find that the immune system‚ Äôs reaction to tissue damage plays a significant role in disease tolerance, along with the effectiveness of the immune response. Bifurcation theory corroborates these findings and displays a region between health and death in which host and pathogen vitals oscillate in the absence of medical intervention, suggesting that damage mitigation and immunity are key players in the maintenance of disease.

Jun Sur Richard Park
University of Iowa
11:40 am

Learning the G-limits in Homogenization Problems via Physics-informed Neural Network

Multiscale equations with scale separation can be approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits requires some other approaches in more general settings.  In this work, we develop efficient physics-informed neural networks (PINNs) algorithm for recovering the G-limit when the multiscale coefficients are unknown and not necessarily periodic. We demonstrate that our approach could produce desirable approximations to the G-limits and, consequently, homogenized solutions.

Yeonjong Shin
Brown University
12:00 pm

Plateau Phenomenon in Gradient Descent Training of ReLU Networks: Explanation, Quantification, and Avoidance

Gradient-based optimization methods result in the loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down. The loss may even appear to stagnate over the period of a large number of epochs, only to then suddenly start to decrease fast again for no apparent reason. This so-called plateau phenomenon manifests itself in many learning tasks. In this talk, we will present our mathematical analysis that identifies and quantifies the root causes of the plateau phenomenon. Based on the insights gained from the mathematical analysis we propose a new iterative training method, the Active Neuron Least Squares (ANLS), characterized by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau.