Padmanabhan Seshaiyer

In this work we present a C-MATH-NN framework that extends a C-MATH framework that was developed in recent years to include prediction using artificial neural networks (NN) in a way that is engaging, interdisciplinary and collaborative to help equip our next generation of students with advanced technological and critical thinking skills motivated by social good. Specifically, the C-MATH framework has successfully helped students understand a real-world Context through a mathematical Model which is then Analyzed mathematically and Tested through appropriate numerical methods with data, and finally this undergraduate research becomes a Habit for students. Furthermore, the explanation of the main components of a simple NN-model serves as an introduction to this popular artificial intelligence tool. This framework has contributed to the success of talented students in mathematical biology research and their academic goals. We present a visual introduction to the architecture of artificial neural networks and its application to disease dynamics for all interested learners. We introduce a simple feed forward physics-informed neural network (PINN) built in MS-Excel that works very well for an epidemiological model and an equivalent Python implementation that is robust and scalable. The products introduced in this work are shared in an online repository with curriculum material for students and instructors that includes MS-Excel workbooks and Python files to facilitate the acquisition of technology tools to explore and use in their own projects.

In this paper, we consider an extended SEIR compartmental model that incorporates young and old interacting subpopulations, allowing for cross-group transmission dynamics. Implicit behavioral changes are included to determine the influence of social behavior on coronavirus transmission dynamics. The basic reproduction number, the average number of secondary cases of infection produced by a single primary case, is derived for both the explicit and implicit model using the next-generation matrix method. We solve the associated differential equation systems and estimate useful parameters in the explicit model using physics-informed neural networks (PINNs). Our results point to how the PINNs approach offers an effective framework to predict the unique parameters of our model, forecast disease progression, and determine the impact of behavioral modifications on the reproduction number and transmission dynamics. Lastly, we have created an interactive dashboard where users can manipulate certain parameters and view the resulting graphs and the reproductive number.

Tumors have garnered significant attention in medical research for disrupting blood flow and lymphatic drainage, forming irregular vasculature that alters transport mechanisms, affecting disease progression and treatment strategies. Additionally, tumor growth affects the peristaltic transport, which plays a crucial role in regulating physiological flows within the tumor microenvironment. The interaction of electric and magnetic fields with peristaltic flow can significantly alter the fluid behavior in these conditions. Modeling of peristaltic transport in tumor microenvironment under electroosmotic flow and magnetic fields requires understanding several interactions: peristaltic motion of the surrounding tissue, electroosmotic effects from charged particles in fluid and walls, and magnetohydrodynamic interactions influencing fluid flow under an external magnetic field. The present study aims to investigate the peristaltic flow under a tumor microenvironment in the presence of externally applied electric and magnetic fields using a mathematical model. An analytical method is used to find the exact solutions of the coupled system of governing equations by applying the lubrication approach and the Debye–Hückel linearization. Furthermore, the results are simulated computationally by using MATLAB. The findings reveal that a higher Hartmann number intensifies magnetic resistance, reducing peristaltic flow, whereas electric fields enhance fluid transport by overcoming this resistance. Additionally, an increase in tumor size and shape further restricts fluid movement, highlighting the obstruction effects of tumor growth. Overall, the present work provides new insights into the combined influence of electroosmosis and magnetohydrodynamics on peristaltic transport within tumor environments. These findings have potential applications in controlling and modulating the physiological fluid flow for improved therapeutic delivery and diagnostics.

Graph convolutional neural networks (GCNs) have shown tremendous promise in addressing data-intensive challenges in recent years. In particular, some attempts have been made to improve predictions of Susceptible-Infected-Recovered (SIR) models by incorporating human mobility between metapopulations and using graph approaches to estimate corresponding hyperparameters. Recently, researchers have found that a hybrid GCN-SIR approach outperformed existing methodologies when used on the data collected on a precinct level in Japan. In our work, we extend this approach to data collected from the continental US, adjusting for the differing mobility patterns and varying policy responses. We also develop the strategy for real-time continuous estimation of the reproduction number and study the accuracy of model predictions for the overall population as well as individual states. Strengths and limitations of the GCN-SIR approach are discussed as a potential candidate for modeling disease dynamics.

Towards developing quantitative models of anti-tumor activities of macrophages, we evaluated the effects of cytokines, tumor exosomes, and polarization states of macrophages in a tumor microenvironemnt using a system of differential equations. We modeled the non-linear dynamics of macrophage polarization states (M0/M1/M2), tumor cell killing by macrophages, and evasion of macrophage mediated killing by tumor originated extracellular vesicle decoys. Solving these coupled differential equations using numerical approaches, showed that the rate of macrophage polarization into the M1 state is the critical determinant of anti-tumor activity mediated by M1 polarized macrophages. To determine what metabolomic factors correlate with the polarization of naïve macrophage into anti-tumor M1 or pro-tumor M2 phenotypes, we performed LC/MS-based untargeted metabolomic analysis. Statistical analysis using Python-Scikit-learn was performed on the metabolomic data from naïve, M1 or M2 polarized murine macrophages followed by multiple feature selection methods. Application of ensemble machine learning methods to both secreted and cell associated metabolites revealed novel molecules of fatty acid metabolism to be the main mediators of polarization. Integration of ensemble machine learning feature-ranking tools into our analysis of metabolomic data identified new potential targets in macrophage metabolism for enhancing anti-tumor activities.

In this work, we employ a governing system of ordinary differential equations (ODEs) to create a mathematical model for getting insights into the dynamics of migration of Ukrainians evacuating due to war. A suitable assumption on coefficients of this model results in the well-known logistic growth. Additionally, stability analyses of equilibrium solutions for these ODEs are performed, and we employ parameter estimation techniques to identify coefficients using online datasets via both a least-squares approach as well as a physics informed neural network approach. Our findings indicate that over time, the daily influx of Ukrainian refugees to Poland stabilizes at a constant rate, represented by an asymptotically stable equilibrium solution.

In an effort to curb the spread of COVID-19, various types of vaccines, including mRNA, viral vectors, and traditional ones, were globally approved and implemented. However, the distribution of vaccines in each country became a critical and determining factor in the disease's evolution. The present study aims to understand the differential impact of the different available vaccine types on disease burden. A proposed mathematical model considers multiple vaccines in a community to analyze the dynamics of COVID-19 transmission in two socioeconomically diverse regions. Secondary incidence data for the cities of Bogotá, Colombia, and New York, USA, from March 2020 to December 2021 were used to estimate vaccine-related parameters and actual transmission rates. The results suggest that although New York has more effective vaccines, higher vaccination rates, and lower poverty rates compared to Bogotá, its disease burden was significantly higher due to higher population density and, consequently, a greater number of contacts. This indicates that while more effective vaccines are crucial to flattening the curve, social distancing measures are equally important for quickly controlling the disease if the vaccination rate is not sufficiently high. Additionally, the model successfully captures the epidemiological behaviour of transmission through the use of vaccines, calculating the basic reproductive number in different scenarios and estimating the parameters of the proposed model.