Year: 2024
Author: Slim Ibrahim, Meili Li, Junling Ma, Kurtis Manke
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 435–452
Abstract
The effective degree SIR model is a precise model for the SIR disease dynamics on a network. The original ODE model is only applicable for a 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 analyze the linear and nonlinear stability of the disease-free steady state of the PDE effective degree model, and show that the basic reproduction number still determines both the linear and the nonlinear stability. Our method also provides a new tool to study the effective degree SIS model, whose basic reproduction number has been elusive so far.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.435
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 435–452
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Generating function effective degree model basic reproduction number spectral stability nonlinear stability steady states.