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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work is supported by SFI grant 06/MI/005.This work was supported by the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland Mathematics Initiative Grant 06/MI/005; by the Ministry of Science and Innovation of Spain via Ramon y Cajal Fellowship RYC-2011-08061 (A. Korobeinikov), and by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A. Melnik).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.