The herpes virus, like many other viruses, can be engineered to target and kill cancer cells. The herpes virus, when loaded with immune stimulating factors, like interleukin 12, can be even more effective at killing cancer cells. We use a mathematical model of oncolytic virus infection and apply it to experimental data from Fukuhara et al. (2023) to assess the effectiveness of different herpes virus strains in treating cancer. We are able to estimate virus characteristics such as viral production rate and infectious lifespan of the different strains, allowing for a quantitative comparison. This type of analysis can help identify which strains are most effective at killing tumors.

Researchers use mathematical models of cancer to study the effectiveness of different regimens of chemotherapy when treating tumors. These models help predict how different treatments affect cancer cell growth in hopes of determining which will effectively kill a tumor. Realistic pulsed drug treatments are computationally expensive and difficult to analyze mathematically. We examine when the effect of a pulsed drug treatment can be well-represented by a constant dose model. Our approach studies treatment applied in various cancer growth patterns, such as exponential, linear, logistic, Mendelsohn, surface, Gompertz, and Bertalanffy models. Mathematically modeling and analyzing the comparison between tumor growth under a pulsed drug treatment and under a constant dose helps us understand when the use of the simpler model can make accurate predictions.

Syncytia are the multinucleated cells that can occur due to virus infection of cells. Mathematical models in the form of ordinary differential equations can be used to simulate the growth of these infections. Several ODE models can explain syncytia growth. Before employing these models on actual data, it is essential to analyze their structural and practical identifiability. Structural identifiability is an inherent property of each model and its parameters, referring to our ability to determine parameter values for the model. Practical Identifiability analysis of a model is concerned with accurately determining parameter values given experimental error. Obtaining accurate parameter values allows us to make conclusions about our data within the context of our model that can provide insight into the nature of the spread of syncytia. These two techniques allow us to determine whether or not the parameters of a model are identifiable with the data we plan to collect. Consequentially, we can plan experiments adequately to truly parameterize the data in the contexts of our model and make accurate conclusions.

Currently, research of gallium oxide (GO) nano- and microcrystals is rapidly expanding with the demand for potential uses. GO has been shown to be a promising material for possible applications in many different fields including photocatalysis, biomedicine, and optoelectronic devices. In our lab (led by Dr. Strzhemechny) we examine both the fundamental (nature of crystal defects) and applied (antibacterial action) properties of GO. During the hydrothermal growth process of GO, we are producing different nano and microscopic morphologies of this material by controlling various growth parameters including varied pH and adding surfactants to the material. The synthesis procedure includes using the precursor material, gallium nitrate hydrate, ammonium hydroxide. We use a calcination furnace that can get to temperatures high enough to effectively synthesize GO. Now, with a thermocouple and pyrometer we can predict outcomes during the calcination step with high accuracy and precision.

This study addresses the escalating concern over the interaction of multiple respiratory viruses by introducing a mathematical model to analyze triple infection dynamics involving influenza (IAV), respiratory syncytial virus (RSV), and SARS-CoV-2. With the ongoing COVID-19 pandemic and the resurgence of RSV, understanding the dynamics of triple infections is critical for public health preparedness. Comprehending the interactions among these viruses is crucial for improving our capacity to forecast and curb disease outbreaks. The central question addressed in this study is how variations in infection rates influence the duration and maximum population size of each virus in a triple infection scenario. Prior research has explored coinfections involving two respiratory viruses, yet triple infections, especially among adults, remain infrequent and poorly elucidated. The urgency to address these questions arises from the potential for overwhelming hospitals and exacerbating disease burden, especially in vulnerable populations. By developing a mathematical model to analyze triple infections, this research aims to provide insights that can inform public health strategies and mitigate the impact of respiratory virus outbreaks. Through extensive simulations, the study evaluates how variations in infection rates influence the duration and maximum population size of each virus. The findings unveil intriguing patterns: while SARS-CoV-2 demonstrates remarkable resilience across various infection rates, influenza and RSV display more nuanced responses, exhibiting sensitivity to changes in transmission rates.