Open AccessLyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility
Author(s) -
A.V. Melnik,
Andrei Korobeinikov,
A.V. Melnik,
Andrei Korobeinikov
Publication year - 2013
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2013.10.369
Subject(s) - lyapunov function , exponential stability , mathematics , stability (learning theory) , control theory (sociology) , computer science , physics , control (management) , nonlinear system , quantum mechanics , machine learning , artificial intelligence
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.