Modeling, Analysis and Prediction of COVID-19 dynamics with interacting subpopulations and human behavior using Physics-Informed Neural Networks

Abstract

The COVID-19 pandemic has underlined the importance of research in epidemiological modeling concerning
adaptive mathematical models, governed by nonlinear ordinary differential equations, that account for evolving
behavioral responses to understand and predict the spread of infectious diseases. In this paper, we consider an extended
SEIR compartmental model that incorporates two interacting subpopulations representing young and old age groups,
allowing for cross-group transmission dynamics. The basic reproduction number, the average number of secondary cases
of infection produced by a single primary case, is derived using the Next Generation Matrix method. Furthermore, we
incorporated a face mask parameter to study the effect of the imposed face mask policy on the reproduction number
which allows for an analysis of the effectiveness of public health interventions. We solve the associated differential
equation system as well as estimate useful parameters in the 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.