Syncytia are a type of multinucleated cell that can be formed by virus infection. Quantifying their growth is of particular interest for understanding virus infection within the body. One useful tool we have to understand the growth of these cells is ordinary differential equation (ODE) models. Current models neglect the regeneration of cells that form the syncytia. To account for regeneration, we will discuss a proposed modification of a basic model for cell-cell fusion, which will consider the addition of a logistic growth term. In addition, we will also consider a non-negligible death rate of syncytia. By making these modifications, we can better replicate syncytia dynamics. We present mathematical analysis of this model, which gives insight into the factors that generate long-term syncytia formation as well as the overall biological characteristics of such an infection.

Graphene quantum dots (GQDs) are spherical nanoparticles comprised of stacked layers of graphene known in part for their biocompatibility and fluorescence, which leads to many potential uses in medicine as a diagnostic tool. Solutions of GQDs are known to fluoresce less when the GQDs are allowed to clump together, leading to processes such as sonication being used to break apart these clumps in research environments. Similarly, the addition of surfactants to a solution of GQDs has also been found to modify fluorescence response of the solution. This research explores the effect of introducing four different human blood proteins on the fluorescence response of reduced graphene quantum dots (rGQDs). Fibrinogen, transferrin, gamma globulin, and albumin were added to samples of rGQDs in increments around their respective concentrations in human blood. Generally, we found that the addition of any of the blood proteins lowered fluorescence response in the visible spectrum. In the near-infrared spectrum, smaller concentrations of blood proteins generally increased fluorescence response, while larger concentrations reduced fluorescence response below the control. This has implications for deep-tissue imaging relying on the near-infrared fluorescence of intravenous GQDs.

Pandemics require quick decisions about how to distribute a limited number of vaccines, even when the disease is not fully understood and vaccine delivery is limited. We create a disease model that divides the population into groups based on how likely they are to be hospitalized and how likely they are to get infected, so we can test different group-based vaccination strategies. We compare vaccinating only one group, simple step-by-step priority policies that vaccinate groups for set time periods, and a sensitivity analysis to see which model factors most affect outcomes.

We find that vaccinating people who are both high-risk for hospitalization and highly likely to become infected leads to the biggest reductions in total hospitalized time and deaths, while vaccinating lower-risk groups gives little improvement in severe outcomes. A short step-by-step policy that quickly prioritizes high-risk groups can reduce infections and deaths within about 20 days. The sensitivity analysis shows that the death rate and the rate at which infected people move into hospitalization have the strongest influence on severe outcomes, showing that hospital and clinical processes matter a lot in addition to vaccination. Overall, these results support clear, practical, and easy-to-apply prioritization rules for reducing severe disease when vaccine supply is limited.

Influenza can cause severe respiratory illness and spreads quickly, making prevention especially important for people at higher risk of complications. Because vaccines are not always fully protective, effective antivirals can provide an added layer of defense before infection begins. CD388 is a new antiviral being tested as a preventive treatment for influenza. In this project, we used a mathematical model to better understand how the drug changes the course of infection inside the body. Viral load data from a human challenge study were fit to a target-cell model with an eclipse phase, allowing us to estimate key infection parameters. Compared to placebo, CD388 lowered peak viral load and reduced overall viral burden by about 22%, largely by suppressing viral production. Bootstrap analysis was used to assess uncertainty in the parameter estimates. These results help explain how CD388 limits viral spread and supports its potential as a prophylactic therapy.

Favipiravir, an antiviral that inhibits viral RNA-dependent RNA polymerase, has demonstrated promise as a therapeutic for RNA viral infections such as SARS-CoV-2. Mathematical modeling of viral kinetics provides a tool for analyzing the progression of viral infections and the action of antiviral drugs. In the present investigation, the viral kinetics of SARS-CoV-2 infection in cynomolgus macaques treated with the antiviral drug favipiravir were analyzed using a target cell-limited mathematical model of viral infection. Parameters of the model representing the dynamics of viral infection and replication were estimated by fitting the model to the viral kinetics data. Statistical resampling techniques were applied to analyze the uncertainty of the parameter estimates and to compare viral kinetics between the different treatment regimens. The results demonstrate that antiviral treatment induces measurable effects on viral kinetic parameters, reflecting dose-response effects on viral infection dynamics.