Mathematical Biosciences and Engineering, 2013, 10(2): 369-378. doi: 10.3934/mbe.2013.10.369.

Primary: 92D30; Secondary: 35F31, 34D23.

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Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility

1. OCCAM, Mathematical Institute, 24 - 29 St Giles', Oxford, OX1 3LB
2. Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona

We consider global asymptotic properties for the SIR and SEIRage structured models for infectious diseases where the susceptibilitydepends on the age. Using the direct Lyapunov method with Volterratype Lyapunov functions, we establish conditions for the global stabilityof a unique endemic steady state and the infection-free steady state.
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Keywords age structured model; Lyapunov function; age structure; global stability; Infectious disease; endemic equilibrium state; compartmentmodel; direct Lyapunov method; distributed population model.

Citation: Andrey V. Melnik, Andrei Korobeinikov. Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility. Mathematical Biosciences and Engineering, 2013, 10(2): 369-378. doi: 10.3934/mbe.2013.10.369

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  • 2. Xia Wang, Yuming Chen, Shengqiang Liu, Global dynamics of a vector-borne disease model with infection ages and general incidence rates, Computational and Applied Mathematics, 2017, 10.1007/s40314-017-0560-8
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