Kayode D. Olumoyin

K. D. Olumoyin, A. Q. M. Khaliq, K. M. Furati

Mutating variants of COVID-19 have been reported across many US states since 2021. In the fight against COVID-19, it has become imperative to study the heterogeneity in the time-varying transmission rates for each variant in the presence of pharmaceutical and non-pharmaceutical mitigation measures. We develop a Susceptible-Exposed-Infected-Recovered mathematical model to highlight the differences in the transmission of the B.1.617.2 delta variant and the original SARS-CoV-2. Theoretical results for the well-posedness of the model are discussed. A Deep neural network is utilized and a deep learning algorithm is developed to learn the time-varying heterogeneous transmission rates for each variant. The accuracy of the algorithm for the model is shown using error metrics in the data-driven simulation for COVID-19 variants in the US states of Florida, Alabama, Tennessee, and Missouri. Short-term forecasting of daily cases is demonstrated using long short term memory neural network and an adaptive neuro-fuzzy inference system.

K. D. Olumoyin

Differential equations are used to model problems that originate in disciplines such as physics, biology, chemistry, and engineering. In recent times, due to the abundance of data, there is an active search for data-driven methods to learn Differential equation models from data. However, many numerical methods often fall short. Advancements in neural networks and deep learning, have motivated a shift towards data-driven deep learning methods of learning differential equations from data. In this work, we propose a forward-Euler based neural network model and test its performance by learning ODEs such as the FitzHugh-Nagumo equations from data using different number of hidden layers and different neural network width.

Kayode Olumoyin, Katarzyna Rejniak

Physics-informed neural networks (PINNs) are neural networks that embed the laws of dynamical systems modeled by differential equations into their loss function as constraints. In this work, we present a PINN framework applied to oncology. Here, we seek to learn time-varying interactions due to a combination therapy in a tumor microenvironment. In oncology, experimental data are often sparse and composed of a few time points of tumor volume. By embedding inductive biases derived from prior information about a dynamical system, we extend the physics-informed neural networks (PINN) and incorporate observed biological constraints as regularization agents. The modified PINN algorithm is able to steer itself to a reasonable solution and can generalize well with only a few training examples. We demonstrate the merit of our approach by learning the dynamics of treatment applied intermittently in an ordinary differential equation (ODE) model of a combination therapy. The algorithm yields a solution to the ODE and time-varying forms of some of the ODE model parameters. We demonstrate a strong convergence using metrics such as the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).