×

Global stability of an SEI epidemic model. (English) Zbl 1045.34025

Summary: This paper considers an SEI epidemic model that incorporates constant recruitment and has infectious force in the latent period and infected period. By means of Lyapunov function and LaSalle’s invariant set theorem, we prove global asymptotical stable results of the disease-free equilibrium and the epidemic equilibrium by using the Poincaré-Bendixson property.

MSC:

34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Li, M. Y.; Muldowney, J. S., Global stability for the SEIR model in epidemiology, Math. Biosci., 125, 155-164 (1995) · Zbl 0821.92022
[2] Li, M. Y.; Muldowney, J. S., A geometric approach to the global-stability problems, SIAM J. Math. Anal., 27, 1070-1083 (1996) · Zbl 0873.34041
[3] Li, M. Y.; Graef, J. R.; Wang, L. C.; Karsai, J., Global dynamics of a SEIR model with a varying total population size, Math. Biosci., 160, 191-213 (1999) · Zbl 0974.92029
[4] Fan, M.; Li, M. Y., Global stability of an SEIS epidemic model with recruitment and a varying total population size, Math. Biosci., 170, 199-208 (2001) · Zbl 1005.92030
[5] Zhang, J., Global analysis of SEI epidemic model with the constant inflows of different compartments, Journal of Xi’an Jiaotong University, 6, 653-656 (2003)
[6] Hale, J. K., Ordinary differential equations (1969), Wiley-Interscience: Wiley-Interscience New York, 296-297 · Zbl 0186.40901
[7] Li MY, Wang L. Global stability in some SEIR epidemic models IMA;126:295-311; Li MY, Wang L. Global stability in some SEIR epidemic models IMA;126:295-311 · Zbl 1022.92035
[8] Muldowney, J. S., Compound matrices and ordinary differential equations, Rocky Mount J. Math., 20, 857-872 (1990) · Zbl 0725.34049
[9] Butler, G. J.; Waltman, P., Persistence in dynamical systems, Proc. Amer. Math. Soc., 96, 425-430 (1986)
[10] Hofbauer, J.; So, J., Uniform persistence and repellors for maps, Proc. Amer. Math. Soc., 107, 1137-1142 (1989) · Zbl 0678.58024
[11] Smith, H. L., Systems of ordinary differential equations which generate an order preserving flow, SIAM Rev., 30, 87-113 (1988) · Zbl 0674.34012
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.