Threshold of Effective Degree SIR Model (Journal of Nonlinear Modeling and Analysis, 2024)
The effective degree SIR model is a precise model for the SIR disease dynamics on a network. The original ODE model is only applicable fora network with finite degree distributions. The new generating function approach rewrites with model as a PDE and allows infinite degree distributions.In this paper, we first prove the existence of a global solution. Then we analyzethe linear and nonlinear stability of the disease-free steady state of the PDEeffective degree model, and show that the basic reproduction number still determines both the linear and the nonlinear stability. Our method also providesa new tool to study the effective degree SIS model, whose basic reproductionnumber has been elusive so far.
Keywords: Generating function; effective degree model; basic reproduction number; spectral stability; nonlinear stability; steady states.