Korobeinikov, A.; Wake, G. C. Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models. (English) Zbl 1022.34044 Appl. Math. Lett. 15, No. 8, 955-960 (2002). The aim of this note is to prove the global stability of the endemic equilibrium states for classical SIR, SIRS and SIS epidemiological models by using the direct Lyapunov metod. Although this result is known in the related literature, the obtention of a Lyapunov function has some interesting advantages like the possibility to compare the rates of convergence towards the equilibrium between the different models. Reviewer: Pedro J.Torres (Granada) Cited in 1 ReviewCited in 138 Documents MSC: 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology 34C60 Qualitative investigation and simulation of ordinary differential equation models Keywords:direct Lyapunov method; Lyapunov functions; epidemiological models; endemic equilibrium state; global stability PDFBibTeX XMLCite \textit{A. Korobeinikov} and \textit{G. C. Wake}, Appl. Math. Lett. 15, No. 8, 955--960 (2002; Zbl 1022.34044) Full Text: DOI References: [1] Lyapunov, A. M., (The General Problem of the Stability of Motion (1992), Taylor & Francis: Taylor & Francis London) · Zbl 0786.70001 [2] Hethcote, H. W.; Levin, S. A., Periodicity in epidemiological models, (Gross, L.; Levin, S. A., Applied Mathematical Ecology (1989), Springer: Springer New York), 193-211 [3] Hethcote, H. W.; Stech, H. W.; van den Driessche, P., Periodicity and stability in epidemiological models: A survey, (Cook, K. L., Differential Equations and Applications in Ecology, Epidemiology and Population Problems (1981), Academic Press: Academic Press New York), 65-85 [4] Mena-Lorca, J.; Hethcote, H. W., Dynamics models of infectious diseases as regulator of population sizes, J. Math. Biol., 30, 693-716 (1992) · Zbl 0748.92012 [5] Busenberg, S.; Cooke, K., (Vertically Transmitted Diseases: Models and Dynamics (1993), Springer: Springer Berlin) · Zbl 0837.92021 [6] Busenberg, S. N.; van den Driessche, P., A method for proving the non-existence of limit cycles, J. Math. Anal. Appl., 172, 463-479 (1993) · Zbl 0779.34026 [7] Anderson, R. M.; May, R. M., (Infectious Diseases in Humans: Dynamics and Control (1991), Oxford University Press: Oxford University Press Oxford) [8] Bailey, N. T.J., (The Mathematical Theory of Infectious Diseases and Its Applications (1975), Griffin: Griffin London) · Zbl 0334.92024 [9] Barbashin, E. A., (Introduction to the Theory of Stability (1970), Wolters-Noordhoff: Wolters-Noordhoff Groningen) [10] La Salle, J.; Lefschetz, S., (Stability by Liapunov’s Direct Method (1961), Academic Press: Academic Press New York) · Zbl 0098.06102 [11] Goh, B.-S., (Management and Analysis of Biological Populations (1980), Elsevier Science: Elsevier Science Amsterdam) [12] Takeuchi, Y., (Global Dynamical Properties of Lotka-Volterra Systems (1996), World Scientific: World Scientific Singapore) · Zbl 0844.34006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.