Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 4, 2011, Pages 1897-1910

  Muroya, Yoshiaki ^a   Enatsu, Yoichi ^a   Nakata, Yukihiko ^b  

^a WASEDA UNIVERSITY   (Japan)

^b BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

Author keywords

Distributed delays; Global asymptotic stability; Nonlinear incidence; SIRS epidemic model

Indexed keywords

CHAOS SOLITONS; DISEASE-FREE EQUILIBRIUM; DISTRIBUTED DELAYS; ENDEMIC EQUILIBRIUM; GLOBAL ASYMPTOTIC STABILITY; LARGE CLASS; MONOTONE ITERATIVE TECHNIQUES; NONLINEAR INCIDENCE; NONLINEAR INCIDENCE RATES; SIRS EPIDEMIC MODEL; SUFFICIENT CONDITIONS;

ASYMPTOTIC STABILITY; SOLITONS;

EPIDEMIOLOGY;

EID: 79955524982     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.12.002     Document Type: Article

References (18)

1. R.M. Anderson, and R.M. May Population biology of infectious diseases: part I Nature 280 1979 361 367
2. E. Beretta, T. Hara, W. Ma, and Y. Takeuchi Global asymptotic stability of an SIR epidemic model with distributed time delay Nonlinear Anal. 47 2001 4107 4115 (Pubitemid 32724581)
3. V. Capasso, and G. Serio A generalization of the KermackMckendrick deterministic epidemic model Math. Biosci. 42 1978 41 61
4. K.L. Cooke Stability analysis for a vector disease model Rocky Mt. J. Math. 9 1979 31 42
5. Hai-Feng Huo, and Zhan-Ping Ma Dynamics of a delayed epidemic model with non-monotonic incidence rate Commun. Nonlinear Sci. Numer. Simul. 15 2010 459 468
6. Y. Jin, W. Wang, and S. Xiao An SIRS model with a nonlinear incidence rate Chaos Solitons Fractals 34 2007 1482 1497 (Pubitemid 46907557)
7. A. Korobeinikov Global properties of infectious disease models with nonlinear incidence Bull. Math. Biol. 69 2007 1871 1886 (Pubitemid 47222242)
8. W.M. Liu, S.A. Levin, and Y. Iwasa Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models J. Math. Biol. 23 1986 187 204 (Pubitemid 16153721)
9. W. Ma, M. Song, and Y. Takeuchi Global stability of an SIR epidemic model with time delay Appl. Math. Lett. 17 2004 1141 1145
10. C.C. McCluskey Complete global stability for an SIR epidemic model with delay-distributed or discrete Nonlinear Anal. Real World Appl. 11 2010 55 59
11. J. Mena-Lorca, and H.W. Hethcote Dynamic models of infectious diseases as regulators of population size J. Math. Biol. 30 1992 693 716
12. Y. Muroya, Y. Enatsu, and Y. Nakata Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate J. Math. Anal. Appl. 2010 10.1016/j.jmaa.2010.010
13. G. Pang, and L. Chen A delayed SIRS epidemic model with pulse vaccination Chaos Solitons Fractals 34 2007 1629 1635 (Pubitemid 46907570)
14. Y. Takeuchi, W. Ma, and E. Beretta Global asymptotic properties of a delay SIR epidemic model with finite incubation times Nonlinear Anal. 42 2000 931 947
15. W. Wang Global behavior of an SEIRS epidemic model with time delays Appl. Math. Lett. 15 2002 423 428
16. D. Xiao, and S. Ruan Global analysis of an epidemic model with nonmonotone incidence rate Math. Biosci. 208 2007 419 429 (Pubitemid 47101853)
17. R. Xu, and Z. Ma Stability of a delayed SIRS epidemic model with a nonlinear incidence rate Chaos Solitons Fractals 41 2009 2319 2325
18. Y. Yang, and D. Xiao Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models Discrete Contin. Dyn. Syst. Ser. B 13 2010 195 211