Lyapunov functions and global properties for SEIR and SEIS epidemic models

Mathematical Medicine and Biology

Volumn 21, Issue 2, 2004, Pages 75-83

  Korobeinikov, Andrei ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Direct Lyapunov method; Endemic equilibrium state global stability; Lyapunov functions

Indexed keywords

EPIDEMIOLOGY; LYAPUNOV METHODS;

DIRECT LYAPUNOV METHODS; ENDEMIC EQUILIBRIUM; ENDEMIC EQUILIBRIUM STATE GLOBAL STABILITY; EPIDEMIC MODELING; EQUILIBRIUM STATE; FUNCTION PROPERTIES; GLOBAL PROPERTIES; GLOBAL STABILITY; LYAPUNOV'S FUNCTIONS; VERTICAL TRANSMISSION;

LYAPUNOV FUNCTIONS;

ARTICLE; BIRTH RATE; COMPARTMENT MODEL; DISEASE TRANSMISSION; EPIDEMIC; GONORRHEA; HUMAN; INFECTION SENSITIVITY; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; MORTALITY; REINFECTION; VERTICAL TRANSMISSION;

EID: 3042703290     PISSN: 14778599     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/21.2.75     Document Type: Article

References (15)

1. Anderson, R. M. & May, R. M. (1991) Infectious Diseases in Humans: Dynamics and Control. Oxford: Oxford University Press.
2. Barbashin, E. A. (1970) Introduction to the Theory of Stability. Groningen: Wolters-Noordhoff.
3. Busenberg, S. & Cooke, K. (1993) Vertically Transmitted Diseases. Berlin: Springer.
4. Goh, B.-S. (1980) Management and Analysis of Biological Populations. Amsterdam: Elsevier.
5. Hethcote, H. W. (2000) The mathematics of infectious diseases. SIAM Rev., 42, 599-653.
6. Hirsch, M. W. (1990) Systems of differential equations which are competitive or cooperative IV: structural stability in three dimensional systems. SIAM J. Math. Anal., 21, 1225-1234.
7. Korobeinikov, A. & Wake, G. C. (2002) Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models. Appl. Math. Lett., 15, 955-961.
8. La Salle, J. & Lefschetz, S. (1961) Stability by Liapunov's Direct Method. New York: Academic.
9. Li, M. Y. & Muldowney, J. S. (1995) Global stability for the SEIR model in epidemiology. Math. Biosci., 125, 155-164.
10. Li, M. Y. et al., (1999) Global dynamics of a SEIR model with varying total population size. Math. Biosci., 160, 191-213.
11. Li, M. Y. et al., (2001) Global dynamics of a SEIR epidemic model with vertical transmission. SIAM J. Appl. Math., 62, 58-69.
12. Li, M. Y. & Wang, L. (2000) Global stability in some SEIR epidemic models. Preprint.
13. Smith, H. L. (1986) Periodic orbits of competitive and cooperative systems. J. Diff. Eqns, 65, 361-373.
14. Takeuchi, Y. (1996) Global Dynamical Properties of Lotka-Volterra Systems. Singapore: World Scientific.
15. Van den Driessche, P. & Watmough, J. (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180, 29-48.