Automated discovery of analytical models for epidemic dynamics on coevolving networks

Abstract

Coevolving network systems provide a framework for modeling the diffusion of social and biological contagions on networks, where network structure is allowed to coevolve with the contagion dynamics, describing phenomena such as the spread of epidemics on social networks where individuals rewire their connectivity to avoid infection. Along with direct computational simulations, coevolving network systems are often formulated in terms of systems of ordinary differential equations in their descriptive statistics. The differential equation approach reduces the computational burden of analyzing the systems, but deriving equations becomes difficult as the underlying model becomes more complicated and the desire for accuracy increases. We present a sparse model identification approach that learns the nonlinear differential equations for coevolving network systems using data from computational simulations. Using this approach, we construct a data-driven system of equations for a coevolving SIS model that reproduces system behavior in both temporal evolution and dependence of steady states on system parameters. Furthermore, we also present the development of a numerical differentiation scheme that performs better for our application than the standard ones in use.