title: Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility.
abstract: 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.
authors: OCCAM, Mathematical Institute, 24 - 29 St Giles, Oxford, OX1 3LB, United Kingdom. andrey.melnik@maths.ox.ac.uk
authors: Andrey V
authors: AV
authors: Melnik
authors: Andrei
authors: A
authors: Korobeinikov
mesh_terms: D000375:Aging / Q000276:immunology*; D003141:Communicable Diseases / Q000453:epidemiology* / Q000276:immunology*; D003198:Computer Simulation; D004198:Disease Susceptibility / Q000453:epidemiology* / Q000276:immunology*; D006801:Humans; D015994:Incidence; D018448:Models, Immunological; D016016:Proportional Hazards Models; D012307:Risk Factors