Coupled contagion dynamics of behavior and disease: A mechanistic learning model approach

During a disease outbreak, such as pandemic influenza, Zika, Ebola and COVID-19, individuals may alter their behaviors, and the social nature of these behaviors, in turn, can mediate or exacerbate the transmission of the disease. Substantial modeling studies have been performed and have uncovered the co-evolution dynamics of collective behaviors of the population and disease transmission risks. In order to reasonably describe the directional feedbacks, these models usually take complicated forms. This paper aims to propose a mechanistic learning model to describe the coupled dynamics of disease transmission and behavior changes during epidemics with simplest assumptions, ensuring that the model has good generalization and low simulation cost. A simple model of two equations, with complicated nonlinear functional terms, can be formulated. Various scenarios for the existence and local (global) stability of five possible equilibria are explored. Complete bifurcation analysis is performed, which illustrates rich co-evolution dynamics of behavior and disease. Finally, an advanced machine learning-based neural ordinary differential equations model is formulated, showing that the model can fit well for single virus strain with multiple waves and exceed more complicated model on performance and efficiency. Future extensions are expected to meet the clear need and offer promising avenues for more comprehensive and integrated disease modeling approaches.