Using Physics-Informed Neural Networks to Model and Simulate the Dynamics of Infectious Diseases in Enclosed Environments

Abstract

Infectious diseases often have high rates of spread in enclosed spaces. Scientists are creating mathematical models to represent the transmission of the disease to better understand how to prevent individuals from being infected. Although previous studies have modeled the diseases in enclosed spaces with differential equations, the parameters for the equations are often assumed or not often known a priori. Instead, we usually have data about the number of people infected that can be used effectively to estimate the optimal parameters. In this study, we used physics-informed neural networks (PINNs) to retrieve the parameters of the differential equations using available infected data. Specifically, we modeled the dynamics of an infectious disease such as COVID in an enclosed space through a compartmental model consisting of five sub-populations including Susceptible, Exposed, Infected, and Recovered for the human population and the Concentration of the contaminant. We used PINNs as an inverse parameter estimation technique to identify optimal transmission and recovery rates in this model both in the absence and presence of contaminants. We studied the impact of the peak number of infected individuals as a function of increased concentration effects. We also calculated the basic reproduction number for the coupled differential equation model that helps us to provide insights into the spread of the epidemic. Our computations suggest that the model created and the PINNs approach employed can be reliable candidates for understanding the spread of diseases in enclosed spaces.