TY - JOUR
T1 - Rate of Convergence to the Disease Free Equilibrium for Multi-Population SIS Networks in the Critical Case
AU - Ye, Mengbin
AU - Anderson, Brian D. O.
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2024/4/24
Y1 - 2024/4/24
N2 - A networked version of the Susceptible-Infected-Susceptible (SIS) deterministic epidemic model is studied. Existing results establish that convergence to an equilibrium occurs exponentially fast, except in the critical case, when the basic reproduction number is equal to 1. This letter uses nonlinear systems and center manifold theory to establish that with such a reproduction number, convergence occurs at a linear rate. Numerical simulations help to illustrate the results.
AB - A networked version of the Susceptible-Infected-Susceptible (SIS) deterministic epidemic model is studied. Existing results establish that convergence to an equilibrium occurs exponentially fast, except in the critical case, when the basic reproduction number is equal to 1. This letter uses nonlinear systems and center manifold theory to establish that with such a reproduction number, convergence occurs at a linear rate. Numerical simulations help to illustrate the results.
KW - Convergence
KW - Diseases
KW - Epidemics
KW - Mathematical models
KW - Sociology
KW - Statistics
KW - Trajectory
KW - Center manifold theory
KW - Meta-population model
KW - Stability of nonlinear system
KW - Susceptible-infected-susceptible
KW - center manifold theory
KW - stability of nonlinear system
KW - meta-population model
KW - susceptible-infected-susceptible
UR - http://www.scopus.com/inward/record.url?scp=85191335819&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2024.3392958
DO - 10.1109/LCSYS.2024.3392958
M3 - Article
SN - 2475-1456
VL - 8
SP - 436
EP - 441
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
ER -