TITLE:
Global Stability in a Graph p-Laplacian SIR Epidemic Model
AUTHORS:
Ling Zhou, Yu Zhang, Zuhan Liu
KEYWORDS:
p-Laplacian, Network, Global Stability, Lyapunov Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.12,
December
26,
2023
ABSTRACT: A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number r0 is greater than 1, while the disease-free equilibrium is globally asymptotically stable if r0 is lower than 1. We extend the stability results of SIR models with graph Laplacian ( p = 2 ) to general graph p-Laplacian.