On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate

Applied Mathematics and Computation

Volumn 217, Issue 8, 2010, Pages 4010-4016

  Buonomo, Bruno ^a   Rionero, Salvatore ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Epidemic model; Lyapunov direct method; Lyapunov function; Nonlinear incidence rate

Indexed keywords

EPIDEMIC MODELS; GLOBAL STABILITY; INCIDENCE RATE; LYAPUNOV; LYAPUNOV DIRECT METHOD; LYAPUNOV STABILITY; MONOTONICITY; NON-LINEAR STABILITIES; NONLINEAR FUNCTIONS; NONLINEAR INCIDENCE RATES; SIRS EPIDEMIC MODEL; SUFFICIENT CONDITIONS;

DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS;

EPIDEMIOLOGY;

EID: 78649989180     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.10.007     Document Type: Article

References (20)

1. R.M. Anderson, and R.M. May Infectious Diseases of Humans: Dynamics and Control 1991 Oxford University Press Oxford
2. S.N. Busenberg, and K. Cooke Vertically Transmitted Diseases Biomathematics vol. 23 1993 Springer-Verlag Berlin
3. V. Capasso Global solution for a diffusive nonlinear deterministic epidemic model SIAM J. Appl. Anal. 35 1978 274 284
4. V. Capasso Mathematical Structures of Epidemic Systems Lecture Notes in Biomath vol. 97 1993 Springer-Verlag Berlin
5. V. Capasso, E. Grosso, and G. Serio I modelli matematici nella indagine epidemiologica Applicazione all'epidemia di colera verificatasi in Bari nel 1973 Annali sclavo 19 1977 193 208
6. V. Capasso, and G. Serio A generalization of the Kermack-Mc Kendrick deterministic epidemic model Math. Biosci. 42 1978 41 61
7. A. d'Onofrio Vaccination policies and nonlinear force of infection: generalization of an observation by Alexander and Moghadas (2004) Appl. Math. Comput. 168 2005 613 622
8. H.W. Hethcote The mathematics of infectious diseases SIAM Rev. 42 2000 599 653
9. A. Korobeinikov Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission Bull. Math. Biol. 30 2006 615 626
10. A. Korobeinikov Global properties of infectious disease models with nonlinear incidence Bull. Math. Biol. 69 2007 1871 1886
11. Y. Jin, W. Wang, and S. Xiao An SIRS model with a nonlinear incidence rate Chaos, Solitons Fractals 34 2007 1482 1497
12. G.H. Li, and Z. Jin Global stability of an SEI epidemic model with general contact rate Chaos, Solitons Fractals 23 2005 997 1004
13. M.Y. Li, J.S. Muldowney, and P. van den Driessche Global stability of SEIRS models in epidemiology Can. Appl. Math. Quart. 7 1999 409 425
14. 2 stability of solutions to a nonlinear binary reaction-diffusion system of P.D.E.s Rend. Math. Acc. Lincei 16 2005 227 238
15. 2 stability analysis for two species dynamics with dispersal Math. Biosci. Eng. 3 2006 189 204
16. 2-stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s to the stability of the solutions to a linear binary system of ODE's J. Math. Anal. Appl. 319 2006 377 397
17. 2-stability analysis for two-species population dynamics in spatial ecology under Neumann boundary data Rend. Circ. Math. Palermo. Ser. II 78 Suppl. 2006 273 283
18. S. Rionero On the nonlinear stability of the critical points of an epidemic SEIR model via a novel Lyapunov function Rend. Acc. Sci. Fis. Nat. Napoli 75 4 2008 115 129
19. P. van den Driessche, and J. Watmough A simple SIS epidemic model with backward bifurcation J. Math. Biol. 40 2000 525 540
20. D. Xiao, and S. Ruan Global analysis of an epidemic model with nonmonotone incidence rate Math. Biosci. 208 2007 129 419