Center for Industrial Mathematics and Statistics » REU 2021 – Modeling SARS-CoV-2 to Predict its Effect on Patients with End-Stage Renal Disease

Veronica Berger

Olivia Tom

Yael Yossefy

Overview

Jndustrial Sponsor: Renal Research Institute

Industrial Liaison: Dr. Alhaji Cherif and Dr. Peter Kontanko

Faculty Advisors: Sam Walcott and Duncan Wright

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2 or COVID-19) emerged in December of 2019, and subsequently profoundly affected public health. Despite mitigation strategies, including effective vaccines, the virus is not yet under control. It is therefore important to study how the virus is transmitted from person to person, as well as how it infects the body. Mathematical models give us a better understanding of the virus and can provide insight into its infection and spread, allowing
us to predict how the disease affects vulnerable populations, i.e., patients with End-Stage Renal Disease, or ESRD. We therefore developed two mathematical models: one describing the population-level spread of the disease, and one describing the dynamics of the virus within an infected patient. The population-level model stratifies the total population into eight different classes and describes the dynamics of these classes with a system of nonlinear differential equations. This model is fit to U.S. cumulative mortality data during the third wave (October 1, 2020 to February 1, 2021), but significantly over- predicts subsequent mortality. Modifying this model to account for mitigation strategies (e.g., social distancing, mask wearing) that become more prevalent during outbreaks allows the model to fit the mortality data beyond the third wave, to successfully predict daily infections, and to capture the wave-like behavior of the disease. Our in-host model uses a similar system of nonlinear differential equations to simulate the interaction between viral particles and various aspects of the innate and adaptive immune response (e.g., T Cells, antibodies, and cytokines). The model fits viral load measurements as a function of time for infected patients from two different sources. Fitting the model to viral load measurements from individual COVID-19 patients allows us to optimize and compare the parameters that vary from person to person. Given the success of these models in fitting data of otherwise healthy individuals, fitting the models to data specific to patients with ESRD can provide insight into transmission, the rate of viral elimination, and other parameters that could be used to inform treatment protocols.